Quelle mpgong.g Sprache: unbekannt
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Spracherkennung für: .g vermutete Sprache: Lisp {Lisp[41] Masm[41] SPS[28]} [Methode: maximale Elemente, drei Dimensionen]
if not IsBound( SnLa_Name ) then
DeclareAttribute( "SnLa_Name", IsLieAlgebra ) ;
fi ;
SNLA_NAMES:=[] ;
BindGlobal( "LieAlgebrasOfMPGong_sList", function(campo)
local e, s, char, z, lambda, tables, t, i, j, l ;
char := Characteristic( campo ) ;
z := Zero( campo ) ;
if char = 2 then
lambda := 1;
else
lambda := - 1 / 2;
fi ;
lambda := lambda * One( campo ) ;
e := dim -> EmptySCTable( dim, z, "antisymmetric" ) ;
s := SetEntrySCTable ;
SNLA_NAMES := [ ] ;
tables := [ ] ;
## The data below on the small nilpotent Lie algebras is taken from M. P.
## Gong, and was converted in a Gap readable format with help by Aldo
## Cristilli.
## Gong, Ming-Peng. Classification of Nilpotent Lie Algebras of
## Dimension 7 (Over Algebraically Closed Fields and R).
## Ph.D. thesis, University of Waterloo, Ontario, Canada, 1998.
## http://etd.uwaterloo.ca/etd/mpgong1998.pdf
## Paragraph 3. 2. 1
## Algebras of Dimensions <= 5
## Dimension 1
Add( SNLA_NAMES, "N1,1" ) ;
t:= e( 1) ;
Add(tables, t) ;
## Dimension 2
## None.
## Dimension 3
Add( SNLA_NAMES, "N3,2" ) ;
t:= e( 3) ;
s( t, 1, 2, [ 1, 3 ] ) ;
Add(tables, t) ;
## Dimension 4
Add( SNLA_NAMES, "N4,2" ) ;
t:= e( 4) ;
for i in [ 2, 3] do
s( t, 1, i, [ 1, i+ 1 ] ) ;
od ;
Add(tables, t) ;
## Dimension 5
Add( SNLA_NAMES, "N5,1" ) ;
t:= e( 5) ;
for i in [ 2, 3, 4] do
s( t, 1, i, [ 1, i+ 1 ] ) ;
od ;
s( t, 2, 3, [ 1, 5 ] ) ;
Add(tables, t) ;
Add( SNLA_NAMES, "N5,2,1" ) ;
t:= e( 5) ;
for i in [ 2, 3, 4] do
s( t, 1, i, [ 1, i+ 1 ] ) ;
od ;
Add(tables, t) ;
Add( SNLA_NAMES, "N5,2,2" ) ;
t:= e( 5) ;
s( t, 1, 2, [ 1, 4 ] ) ;
s( t, 1, 4, [ 1, 5 ] ) ;
s( t, 2, 3, [ 1, 5 ] ) ;
Add(tables, t) ;
Add( SNLA_NAMES, "N5,2,3" ) ;
t:= e( 5) ;
for i in [ 2, 3] do
s( t, 1, i, [ 1, i+ 1 ] ) ;
od ;
s( t, 2, 3, [ 1, 5 ] ) ;
Add(tables, t) ;
Add( SNLA_NAMES, "N5,3,1" ) ;
t:= e( 5) ;
s( t, 1, 2, [ 1, 5 ] ) ;
s( t, 3, 4, [ 1, 5 ] ) ;
Add(tables, t) ;
Add( SNLA_NAMES, "N5,3,2" ) ;
t:= e( 5) ;
s( t, 1, 2, [ 1, 4 ] ) ;
s( t, 1, 3, [ 1, 5 ] ) ;
Add(tables, t) ;
## Paragraph 3. 2. 2
## Algebras of Dimension 6 over Algebraically Closed Fields of char <> 2
Add( SNLA_NAMES, "N6,1,1" ) ;
t:= e( 6) ;
for i in [ 2 .. 5] do
s( t, 1, i, [ 1, i+ 1 ] ) ;
od ;
for i in [ 3, 4] do
s( t, 2, i, [ 1, i+ 2 ] ) ;
od ;
Add(tables, t) ;
Add( SNLA_NAMES, "N6,1,2" ) ;
t:= e( 6) ;
for i in [ 2, 3, 4] do
s( t, 1, i, [ 1, i+ 1 ] ) ;
od ;
s( t, 2, 3, [ 1, 5 ] ) ;
s( t, 2, 5, [ 1, 6 ] ) ;
s( t, 3, 4, [ - 1, 6 ] ) ;
Add(tables, t) ;
Add( SNLA_NAMES, "N6,1,3" ) ;
t:= e( 6) ;
for i in [ 2 .. 5] do
s( t, 1, i, [ 1, i+ 1 ] ) ;
od ;
s( t, 2, 3, [ 1, 6 ] ) ;
Add(tables, t) ;
Add( SNLA_NAMES, "N6,1,4" ) ;
t:= e( 6) ;
s( t, 1, 2, [ 1, 3 ] ) ;
s( t, 1, 3, [ 1, 4 ] ) ;
s( t, 1, 4, [ 1, 6 ] ) ;
s( t, 2, 3, [ 1, 6 ] ) ;
s( t, 2, 5, [ 1, 6 ] ) ;
Add(tables, t) ;
Add( SNLA_NAMES, "N6,2,1" ) ;
t:= e( 6) ;
for i in [ 2 .. 5] do
s( t, 1, i, [ 1, i+ 1 ] ) ;
od ;
Add(tables, t) ;
Add( SNLA_NAMES, "N6,2,2" ) ;
t:= e( 6) ;
for i in [ 2, 3, 4] do
s( t, 1, i, [ 1, i+ 1 ] ) ;
od ;
s( t, 2, 5, [ 1, 6 ] ) ;
s( t, 3, 4, [ - 1, 6 ] ) ;
Add(tables, t) ;
Add( SNLA_NAMES, "N6,2,3" ) ;
t:= e( 6) ;
s( t, 1, 2, [ 1, 4 ] ) ;
for i in [ 4, 5] do
s( t, 1, i, [ 1, i+ 1 ] ) ;
od ;
s( t, 2, 3, [ 1, 5 ] ) ;
s( t, 3, 4, [ - 1, 6 ] ) ;
Add(tables, t) ;
Add( SNLA_NAMES, "N6,2,4" ) ;
t:= e( 6) ;
s( t, 1, 2, [ 1, 3 ] ) ;
s( t, 1, 3, [ 1, 4 ] ) ;
s( t, 1, 4, [ 1, 6 ] ) ;
s( t, 2, 5, [ 1, 6 ] ) ;
Add(tables, t) ;
Add( SNLA_NAMES, "N6,2,5" ) ;
t:= e( 6) ;
for i in [ 2, 3, 5] do
s( t, 1, i, [ 1, i+ 1 ] ) ;
od ;
for j in [ 3, 4] do
s( t, 2, j, [ 1, j+ 2 ] ) ;
od ;
Add(tables, t) ;
Add( SNLA_NAMES, "N6,2,6" ) ;
t:= e( 6) ;
s( t, 1, 2, [ 1, 4 ] ) ;
s( t, 1, 3, [ 1, 5 ] ) ;
s( t, 1, 4, [ 1, 6 ] ) ;
s( t, 3, 5, [ 1, 6 ] ) ;
Add(tables, t) ;
Add( SNLA_NAMES, "N6,2,7" ) ;
t:= e( 6) ;
for i in [ 2, 3, 4] do
s( t, 1, i, [ 1, i+ 1 ] ) ;
od ;
s( t, 2, 3, [ 1, 6 ] ) ;
Add(tables, t) ;
Add( SNLA_NAMES, "N6,2,8" ) ;
t:= e( 6) ;
s( t, 1, 2, [ 1, 3 ] ) ;
s( t, 1, 3, [ 1, 5 ] ) ;
s( t, 1, 4, [ 1, 6 ] ) ;
s( t, 2, 4, [ 1, 5 ] ) ;
Add(tables, t) ;
Add( SNLA_NAMES, "N6,2,9" ) ;
t:= e( 6) ;
s( t, 1, 2, [ 1, 3 ] ) ;
s( t, 1, 3, [ 1, 5 ] ) ;
s( t, 2, 3, [ 1, 6 ] ) ;
s( t, 2, 4, [ 1, 6 ] ) ;
Add(tables, t) ;
Add( SNLA_NAMES, "N6,2,10" ) ;
t:= e( 6) ;
s( t, 1, 2, [ 1, 3 ] ) ;
s( t, 1, 3, [ 1, 5 ] ) ;
s( t, 2, 3, [ 1, 6 ] ) ;
s( t, 2, 4, [ 1, 5 ] ) ;
Add(tables, t) ;
Add( SNLA_NAMES, "N6,3,1" ) ;
t:= e( 6) ;
for i in [ 2, 3] do
s( t, 1, i, [ 1, i+ 2 ] ) ;
od ;
s( t, 2, 5, [ 1, 6 ] ) ;
s( t, 3, 4, [ 1, 6 ] ) ;
Add(tables, t) ;
Add( SNLA_NAMES, "N6,3,2" ) ;
t:= e( 6) ;
s( t, 1, 2, [ 1, 3 ] ) ;
s( t, 1, 3, [ 1, 6 ] ) ;
s( t, 4, 5, [ 1, 6 ] ) ;
Add(tables, t) ;
Add( SNLA_NAMES, "N6,3,3" ) ;
t:= e( 6) ;
s( t, 1, 2, [ 1, 3 ] ) ;
s( t, 1, 4, [ 1, 6 ] ) ;
s( t, 2, 3, [ 1, 5 ] ) ;
Add(tables, t) ;
Add( SNLA_NAMES, "N6,3,4" ) ;
t:= e( 6) ;
s( t, 1, 2, [ 1, 3 ] ) ;
s( t, 2, 3, [ 1, 5 ] ) ;
s( t, 2, 4, [ 1, 6 ] ) ;
Add(tables, t) ;
Add( SNLA_NAMES, "N6,3,5" ) ;
t:= e( 6) ;
s( t, 1, 2, [ 1, 5 ] ) ;
s( t, 1, 4, [ 1, 6 ] ) ;
s( t, 2, 3, [ 1, 6 ] ) ;
Add(tables, t) ;
Add( SNLA_NAMES, "N6,3,6" ) ;
t:= e( 6) ;
s( t, 1, 2, [ 1, 4 ] ) ;
s( t, 1, 3, [ 1, 5 ] ) ;
s( t, 2, 3, [ 1, 6 ] ) ;
Add(tables, t) ;
## Paragraph 3. 2. 3
## Algebras of Dimension 6 over Algebraically Closed Fields of char = 2
## In addition to the algebras over algebraically closed fields of
## char <> 2, ## we have the following 5 extra indecomposable algebras
## for char = 2:
if char = 2 then
Add( SNLA_NAMES, "A" ) ;
t:= e( 6) ;
for i in [ 2 .. 5] do
s( t, 1, i, [ 1, i+ 1 ] ) ;
od ;
s( t, 2, 3, [ 1, 5, 1, 6 ] ) ;
s( t, 2, 4, [ 1, 6 ] ) ;
Add(tables, t) ;
## Remark: When char <> 2, this algebra is isomorphic to N6 ;1;1.
Add( SNLA_NAMES, "B" ) ;
t:= e( 6) ;
s( t, 1, 2, [ 1, 4 ] ) ;
s( t, 1, 4, [ 1, 5 ] ) ;
s( t, 1, 5, [ 1, 6 ] ) ;
s( t, 2, 3, [ 1, 5, 1, 6 ] ) ;
s( t, 3, 4, [ - 1, 6 ] ) ;
Add(tables, t) ;
## Remark: When char <> 2, this algebra is isomorphic to N6 ;2;3.
Add( SNLA_NAMES, "C" ) ;
t:= e( 6) ;
for i in [ 2, 3, 5] do
s( t, 1, i, [ 1, i+ 1 ] ) ;
od ;
s( t, 2, 3, [ 1, 5 ] ) ;
s( t, 2, 4, [ 1, 6 ] ) ;
s( t, 2, 5, [ 1, 6 ] ) ;
Add(tables, t) ;
## Remark: When char <> 2, this algebra is isomorphic to N6 ;2;5.
Add( SNLA_NAMES, "D" ) ;
t:= e( 6) ;
s( t, 1, 2, [ 1, 4 ] ) ;
s( t, 1, 3, [ 1, 5 ] ) ;
s( t, 2, 5, [ 1, 6 ] ) ;
s( t, 3, 4, [ 1, 6 ] ) ;
s( t, 3, 5, [ 1, 6 ] ) ;
Add(tables, t) ;
## Remark: When char <> 2, this algebra is isomorphic to N6 ;3;1.
Add( SNLA_NAMES, "E" ) ;
t:= e( 6) ;
s( t, 1, 2, [ 1, 3 ] ) ;
s( t, 1, 3, [ 1, 5 ] ) ;
s( t, 1, 4, [ 1, 6 ] ) ;
s( t, 2, 3, [ 1, 6 ] ) ;
s( t, 2, 4, [ 1, 5 ] ) ;
Add(tables, t) ;
## Remark: When char <> 2, this algebra is isomorphic to N6 ;2;10.
fi ;
## Paragraph 7. 4
## Four More Real Algebras and Their Extensions
## In the real field R, apart from all the algebras already listed over C,
## we have 4 more algebras, which we will list in the following, ... . The
## notation La means that, as a Lie algebras over R, La and L are
## nonisomorphic algebras, but are isomorphic over the complex field C.
Add( SNLA_NAMES, "N6,2,5a" ) ;
t:= e( 6) ;
for i in [ 2, 3] do
s( t, 1, i, [ 1, i+ 1 ] ) ;
od ;
s( t, 1, 4, [ - 1, 6 ] ) ;
s( t, 2, 3, [ 1, 5 ] ) ;
s( t, 2, 5, [ - 1, 6 ] ) ;
Add(tables, t) ;
Add( SNLA_NAMES, "N6,2,9a" ) ;
t:= e( 6) ;
s( t, 1, 2, [ 1, 3 ] ) ;
for i in [ 3, 4] do
s( t, 1, i, [ 1, i+ 2 ] ) ;
od ;
s( t, 2, 3, [ - 1, 6 ] ) ;
s( t, 2, 4, [ 1, 5 ] ) ;
Add(tables, t) ;
Add( SNLA_NAMES, "N6,3,1a" ) ;
t:= e( 6) ;
for i in [ 2, 3] do
s( t, 1, i, [ 1, i+ 2 ] ) ;
od ;
s( t, 2, 4, [ 1, 6 ] ) ;
s( t, 3, 5, [ 1, 6 ] ) ;
Add(tables, t) ;
Add( SNLA_NAMES, "N6,4,4a" ) ;
t:= e( 6) ;
s( t, 1, 3, [ 1, 5 ] ) ;
s( t, 2, 4, [ 1, 5 ] ) ;
s( t, 1, 4, [ - 1, 6 ] ) ;
s( t, 2, 3, [ 1, 6 ] ) ;
Add(tables, t) ;
## Paragraph 4. 1:
## List of 7-Dimensional Indecomposable Nilpotent Lie Algebras
## over Algebraically Closed Fields (char <> 2)
## Upper Central Series Dimensions ( 37)
Add( SNLA_NAMES, "37A" ) ;
t:= e( 7) ;
s( t, 1, 2, [ 1, 5 ] ) ;
s( t, 2, 3, [ 1, 6 ] ) ;
s( t, 2, 4, [ 1, 7 ] ) ;
Add(tables, t) ;
Add( SNLA_NAMES, "37B" ) ;
t:= e( 7) ;
s( t, 1, 2, [ 1, 5 ] ) ;
s( t, 2, 3, [ 1, 6 ] ) ;
s( t, 3, 4, [ 1, 7 ] ) ;
Add(tables, t) ;
Add( SNLA_NAMES, "37C" ) ;
t:= e( 7) ;
s( t, 1, 2, [ 1, 5 ] ) ;
s( t, 2, 3, [ 1, 6 ] ) ;
s( t, 2, 4, [ 1, 7 ] ) ;
s( t, 3, 4, [ 1, 5 ] ) ;
Add(tables, t) ;
Add( SNLA_NAMES, "37D" ) ;
t:= e( 7) ;
s( t, 1, 2, [ 1, 5 ] ) ;
s( t, 1, 3, [ 1, 6 ] ) ;
s( t, 2, 4, [ 1, 7 ] ) ;
s( t, 3, 4, [ 1, 5 ] ) ;
Add(tables, t) ;
## Upper Central Series Dimensions ( 357)
Add( SNLA_NAMES, "357A" ) ;
t:= e( 7) ;
s( t, 1, 2, [ 1, 3 ] ) ;
s( t, 1, 3, [ 1, 5 ] ) ;
s( t, 1, 4, [ 1, 7 ] ) ;
s( t, 2, 4, [ 1, 6 ] ) ;
Add(tables, t) ;
Add( SNLA_NAMES, "357B" ) ;
t:= e( 7) ;
s( t, 1, 2, [ 1, 3 ] ) ;
s( t, 1, 3, [ 1, 5 ] ) ;
s( t, 1, 4, [ 1, 7 ] ) ;
s( t, 2, 3, [ 1, 6 ] ) ;
Add(tables, t) ;
Add( SNLA_NAMES, "357C" ) ;
t:= e( 7) ;
s( t, 1, 2, [ 1, 3 ] ) ;
s( t, 1, 3, [ 1, 5 ] ) ;
s( t, 1, 4, [ 1, 7 ] ) ;
s( t, 2, 3, [ 1, 6 ] ) ;
s( t, 2, 4, [ 1, 5 ] ) ;
Add(tables, t) ;
## Upper Central Series Dimensions ( 27)
Add( SNLA_NAMES, "27A" ) ;
t:= e( 7) ;
s( t, 1, 2, [ 1, 6 ] ) ;
s( t, 1, 4, [ 1, 7 ] ) ;
s( t, 3, 5, [ 1, 7 ] ) ;
Add(tables, t) ;
Add( SNLA_NAMES, "27B" ) ;
t:= e( 7) ;
s( t, 1, 2, [ 1, 6 ] ) ;
s( t, 1, 5, [ 1, 7 ] ) ;
s( t, 2, 3, [ 1, 7 ] ) ;
s( t, 3, 4, [ 1, 6 ] ) ;
Add(tables, t) ;
## Upper Central Series Dimensions ( 257)
Add( SNLA_NAMES, "257A" ) ;
t:= e( 7) ;
s( t, 1, 2, [ 1, 3 ] ) ;
s( t, 1, 3, [ 1, 6 ] ) ;
s( t, 1, 5, [ 1, 7 ] ) ;
s( t, 2, 4, [ 1, 6 ] ) ;
Add(tables, t) ;
Add( SNLA_NAMES, "257B" ) ;
t:= e( 7) ;
s( t, 1, 2, [ 1, 3 ] ) ;
s( t, 1, 3, [ 1, 6 ] ) ;
s( t, 1, 4, [ 1, 7 ] ) ;
s( t, 2, 5, [ 1, 7 ] ) ;
Add(tables, t) ;
Add( SNLA_NAMES, "257C" ) ;
t:= e( 7) ;
s( t, 1, 2, [ 1, 3 ] ) ;
s( t, 1, 3, [ 1, 6 ] ) ;
s( t, 2, 4, [ 1, 6 ] ) ;
s( t, 2, 5, [ 1, 7 ] ) ;
Add(tables, t) ;
Add( SNLA_NAMES, "257D" ) ;
t:= e( 7) ;
s( t, 1, 2, [ 1, 3 ] ) ;
s( t, 1, 3, [ 1, 6 ] ) ;
s( t, 1, 4, [ 1, 7 ] ) ;
s( t, 2, 4, [ 1, 6 ] ) ;
s( t, 2, 5, [ 1, 7 ] ) ;
Add(tables, t) ;
Add( SNLA_NAMES, "257E" ) ;
t:= e( 7) ;
s( t, 1, 2, [ 1, 3 ] ) ;
s( t, 1, 3, [ 1, 6 ] ) ;
s( t, 2, 4, [ 1, 7 ] ) ;
s( t, 4, 5, [ 1, 6 ] ) ;
Add(tables, t) ;
Add( SNLA_NAMES, "257F" ) ;
t:= e( 7) ;
s( t, 1, 2, [ 1, 3 ] ) ;
s( t, 2, 3, [ 1, 6 ] ) ;
s( t, 2, 4, [ 1, 7 ] ) ;
s( t, 4, 5, [ 1, 6 ] ) ;
Add(tables, t) ;
Add( SNLA_NAMES, "257G" ) ;
t:= e( 7) ;
s( t, 1, 2, [ 1, 3 ] ) ;
s( t, 1, 3, [ 1, 6 ] ) ;
s( t, 1, 5, [ 1, 7 ] ) ;
s( t, 2, 4, [ 1, 7 ] ) ;
s( t, 4, 5, [ 1, 6 ] ) ;
Add(tables, t) ;
Add( SNLA_NAMES, "257H" ) ;
t:= e( 7) ;
s( t, 1, 2, [ 1, 3 ] ) ;
s( t, 1, 3, [ 1, 6 ] ) ;
s( t, 2, 4, [ 1, 6 ] ) ;
s( t, 4, 5, [ 1, 7 ] ) ;
Add(tables, t) ;
Add( SNLA_NAMES, "257I" ) ;
t:= e( 7) ;
s( t, 1, 2, [ 1, 3 ] ) ;
s( t, 1, 3, [ 1, 6 ] ) ;
s( t, 1, 4, [ 1, 6 ] ) ;
s( t, 1, 5, [ 1, 7 ] ) ;
s( t, 2, 3, [ 1, 7 ] ) ;
Add(tables, t) ;
Add( SNLA_NAMES, "257J" ) ;
t:= e( 7) ;
s( t, 1, 2, [ 1, 3 ] ) ;
s( t, 1, 3, [ 1, 6 ] ) ;
s( t, 1, 5, [ 1, 7 ] ) ;
s( t, 2, 3, [ 1, 7 ] ) ;
s( t, 2, 4, [ 1, 6 ] ) ;
Add(tables, t) ;
Add( SNLA_NAMES, "257K" ) ;
t:= e( 7) ;
s( t, 1, 2, [ 1, 3 ] ) ;
s( t, 1, 3, [ 1, 6 ] ) ;
s( t, 2, 3, [ 1, 7 ] ) ;
s( t, 4, 5, [ 1, 7 ] ) ;
Add(tables, t) ;
Add( SNLA_NAMES, "257L" ) ;
t:= e( 7) ;
s( t, 1, 2, [ 1, 3 ] ) ;
s( t, 1, 3, [ 1, 6 ] ) ;
s( t, 2, 3, [ 1, 7 ] ) ;
s( t, 2, 4, [ 1, 6 ] ) ;
s( t, 4, 5, [ 1, 7 ] ) ;
Add(tables, t) ;
## Upper Central Series Dimensions ( 247)
Add( SNLA_NAMES, "247A" ) ;
t:= e( 7) ;
for i in [ 2, 3, 4, 5] do
s( t, 1, i, [ 1, i+ 2 ] ) ;
od ;
Add(tables, t) ;
Add( SNLA_NAMES, "247B" ) ;
t:= e( 7) ;
for i in [ 2, 3, 4] do
s( t, 1, i, [ 1, i+ 2 ] ) ;
od ;
s( t, 3, 5, [ 1, 7 ] ) ;
Add(tables, t) ;
Add( SNLA_NAMES, "247C" ) ;
t:= e( 7) ;
for i in [ 2, 3, 4] do
s( t, 1, i, [ 1, i+ 2 ] ) ;
od ;
s( t, 1, 5, [ 1, 7 ] ) ;
s( t, 3, 5, [ 1, 6 ] ) ;
Add(tables, t) ;
Add( SNLA_NAMES, "247D" ) ;
t:= e( 7) ;
for i in [ 2, 3] do
s( t, 1, i, [ 1, i+ 2 ] ) ;
od ;
s( t, 1, 4, [ 1, 6 ] ) ;
s( t, 2, 5, [ 1, 7 ] ) ;
s( t, 3, 4, [ 1, 7 ] ) ;
Add(tables, t) ;
Add( SNLA_NAMES, "247E" ) ;
t:= e( 7) ;
for i in [ 2, 3, 4] do
s( t, 1, i, [ 1, i+ 2 ] ) ;
od ;
s( t, 1, 5, [ 1, 6 ] ) ;
s( t, 2, 5, [ 1, 7 ] ) ;
s( t, 3, 4, [ 1, 7 ] ) ;
Add(tables, t) ;
Add( SNLA_NAMES, "247F" ) ;
t:= e( 7) ;
for i in [ 2, 3] do
s( t, 1, i, [ 1, i+ 2 ] ) ;
od ;
s( t, 2, 4, [ 1, 6 ] ) ;
s( t, 2, 5, [ 1, 7 ] ) ;
s( t, 3, 4, [ 1, 7 ] ) ;
s( t, 3, 5, [ 1, 6 ] ) ;
Add(tables, t) ;
Add( SNLA_NAMES, "247G" ) ;
t:= e( 7) ;
for i in [ 2, 3, 4] do
s( t, 1, i, [ 1, i+ 2 ] ) ;
od ;
s( t, 1, 5, [ 1, 6 ] ) ;
s( t, 2, 4, [ 1, 6 ] ) ;
s( t, 2, 5, [ 1, 7 ] ) ;
s( t, 3, 4, [ 1, 7 ] ) ;
s( t, 3, 5, [ 1, 6 ] ) ;
Add(tables, t) ;
Add( SNLA_NAMES, "247H" ) ;
t:= e( 7) ;
for i in [ 2, 3, 4] do
s( t, 1, i, [ 1, i+ 2 ] ) ;
od ;
s( t, 2, 4, [ 1, 6 ] ) ;
s( t, 2, 5, [ 1, 7 ] ) ;
s( t, 3, 4, [ 1, 7 ] ) ;
s( t, 3, 5, [ 1, 6 ] ) ;
Add(tables, t) ;
Add( SNLA_NAMES, "247I" ) ;
t:= e( 7) ;
for i in [ 2, 3] do
s( t, 1, i, [ 1, i+ 2 ] ) ;
od ;
s( t, 2, 5, [ 1, 6 ] ) ;
s( t, 3, 4, [ 1, 6 ] ) ;
s( t, 3, 5, [ 1, 7 ] ) ;
Add(tables, t) ;
Add( SNLA_NAMES, "247J" ) ;
t:= e( 7) ;
for i in [ 2, 3] do
s( t, 1, i, [ 1, i+ 2 ] ) ;
od ;
s( t, 1, 5, [ 1, 6 ] ) ;
s( t, 2, 5, [ 1, 7 ] ) ;
s( t, 3, 4, [ 1, 7 ] ) ;
s( t, 3, 5, [ 1, 6 ] ) ;
Add(tables, t) ;
Add( SNLA_NAMES, "247K" ) ;
t:= e( 7) ;
for i in [ 2, 3, 4] do
s( t, 1, i, [ 1, i+ 2 ] ) ;
od ;
s( t, 2, 5, [ 1, 7 ] ) ;
s( t, 3, 4, [ 1, 7 ] ) ;
s( t, 3, 5, [ 1, 6 ] ) ;
Add(tables, t) ;
Add( SNLA_NAMES, "247L" ) ;
t:= e( 7) ;
for i in [ 2, 3, 4, 5] do
s( t, 1, i, [ 1, i+ 2 ] ) ;
od ;
s( t, 2, 3, [ 1, 6 ] ) ;
Add(tables, t) ;
Add( SNLA_NAMES, "247M" ) ;
t:= e( 7) ;
for i in [ 2, 3, 4] do
s( t, 1, i, [ 1, i+ 2 ] ) ;
od ;
s( t, 2, 3, [ 1, 6 ] ) ;
s( t, 3, 5, [ 1, 7 ] ) ;
Add(tables, t) ;
Add( SNLA_NAMES, "247N" ) ;
t:= e( 7) ;
for i in [ 2, 3] do
s( t, 1, i, [ 1, i+ 2 ] ) ;
od ;
s( t, 1, 5, [ 1, 6 ] ) ;
s( t, 2, 3, [ 1, 7 ] ) ;
s( t, 2, 4, [ 1, 6 ] ) ;
Add(tables, t) ;
Add( SNLA_NAMES, "247O" ) ;
t:= e( 7) ;
for i in [ 2, 3, 4] do
s( t, 1, i, [ 1, i+ 2 ] ) ;
od ;
s( t, 1, 5, [ 1, 7 ] ) ;
s( t, 2, 3, [ 1, 7 ] ) ;
s( t, 3, 5, [ 1, 6 ] ) ;
Add(tables, t) ;
Add( SNLA_NAMES, "247P" ) ;
t:= e( 7) ;
for i in [ 2, 3] do
s( t, 1, i, [ 1, i+ 2 ] ) ;
od ;
s( t, 2, 3, [ 1, 6 ] ) ;
s( t, 2, 5, [ 1, 7 ] ) ;
s( t, 3, 4, [ 1, 7 ] ) ;
Add(tables, t) ;
Add( SNLA_NAMES, "247Q" ) ;
t:= e( 7) ;
for i in [ 2, 3, 4] do
s( t, 1, i, [ 1, i+ 2 ] ) ;
od ;
s( t, 2, 3, [ 1, 6 ] ) ;
s( t, 2, 5, [ 1, 7 ] ) ;
s( t, 3, 4, [ 1, 7 ] ) ;
Add(tables, t) ;
Add( SNLA_NAMES, "247R" ) ;
t:= e( 7) ;
for i in [ 2, 3, 4] do
s( t, 1, i, [ 1, i+ 2 ] ) ;
od ;
s( t, 1, 5, [ 1, 6 ] ) ;
s( t, 2, 3, [ 1, 6 ] ) ;
s( t, 2, 5, [ 1, 7 ] ) ;
s( t, 3, 4, [ 1, 7 ] ) ;
Add(tables, t) ;
## Upper Central Series Dimensions ( 2457)
Add( SNLA_NAMES, "2457A" ) ;
t:= e( 7) ;
for i in [ 2, 3] do
s( t, 1, i, [ 1, i+ 1 ] ) ;
od ;
for i in [ 4, 5] do
s( t, 1, i, [ 1, i+ 2 ] ) ;
od ;
Add(tables, t) ;
Add( SNLA_NAMES, "2457B" ) ;
t:= e( 7) ;
for i in [ 2, 3] do
s( t, 1, i, [ 1, i+ 1 ] ) ;
od ;
s( t, 1, 4, [ 1, 7 ] ) ;
s( t, 2, 5, [ 1, 6 ] ) ;
Add(tables, t) ;
Add( SNLA_NAMES, "2457C" ) ;
t:= e( 7) ;
for i in [ 2, 3] do
s( t, 1, i, [ 1, i+ 1 ] ) ;
od ;
for i in [ 4, 5] do
s( t, 1, i, [ 1, i+ 2 ] ) ;
od ;
s( t, 2, 5, [ 1, 6 ] ) ;
Add(tables, t) ;
Add( SNLA_NAMES, "2457D" ) ;
t:= e( 7) ;
for i in [ 2, 3] do
s( t, 1, i, [ 1, i+ 1 ] ) ;
od ;
for i in [ 4, 5] do
s( t, 1, i, [ 1, i+ 2 ] ) ;
od ;
s( t, 2, 3, [ 1, 6 ] ) ;
s( t, 2, 5, [ 1, 6 ] ) ;
Add(tables, t) ;
Add( SNLA_NAMES, "2457E" ) ;
t:= e( 7) ;
for i in [ 2, 3] do
s( t, 1, i, [ 1, i+ 1 ] ) ;
od ;
s( t, 1, 4, [ 1, 7 ] ) ;
s( t, 2, 3, [ 1, 6 ] ) ;
s( t, 2, 5, [ 1, 6 ] ) ;
Add(tables, t) ;
Add( SNLA_NAMES, "2457F" ) ;
t:= e( 7) ;
for i in [ 2, 3] do
s( t, 1, i, [ 1, i+ 1 ] ) ;
od ;
for i in [ 4, 5] do
s( t, 1, i, [ 1, i+ 2 ] ) ;
od ;
s( t, 2, 3, [ 1, 6 ] ) ;
Add(tables, t) ;
Add( SNLA_NAMES, "2457G" ) ;
t:= e( 7) ;
for i in [ 2, 3] do
s( t, 1, i, [ 1, i+ 1 ] ) ;
od ;
s( t, 1, 4, [ 1, 7 ] ) ;
s( t, 1, 5, [ 1, 6 ] ) ;
s( t, 2, 3, [ 1, 6 ] ) ;
Add(tables, t) ;
Add( SNLA_NAMES, "2457H" ) ;
t:= e( 7) ;
for i in [ 2, 3] do
s( t, 1, i, [ 1, i+ 1 ] ) ;
od ;
s( t, 1, 4, [ 1, 7 ] ) ;
s( t, 2, 3, [ 1, 6 ] ) ;
s( t, 2, 5, [ 1, 7 ] ) ;
Add(tables, t) ;
Add( SNLA_NAMES, "2457I" ) ;
t:= e( 7) ;
for i in [ 2, 3] do
s( t, 1, i, [ 1, i+ 1 ] ) ;
od ;
s( t, 1, 4, [ 1, 6 ] ) ;
s( t, 2, 3, [ 1, 6 ] ) ;
s( t, 2, 5, [ 1, 7 ] ) ;
Add(tables, t) ;
Add( SNLA_NAMES, "2457J" ) ;
t:= e( 7) ;
for i in [ 2, 3] do
s( t, 1, i, [ 1, i+ 1 ] ) ;
od ;
s( t, 1, 4, [ 1, 6 ] ) ;
s( t, 2, 3, [ 1, 6, 1, 7 ] ) ;
s( t, 2, 5, [ 1, 7 ] ) ;
Add(tables, t) ;
Add( SNLA_NAMES, "2457K" ) ;
t:= e( 7) ;
for i in [ 2, 3] do
s( t, 1, i, [ 1, i+ 1 ] ) ;
od ;
s( t, 1, 4, [ 1, 7 ] ) ;
s( t, 1, 5, [ 1, 6 ] ) ;
s( t, 2, 3, [ 1, 6 ] ) ;
s( t, 2, 5, [ 1, 7 ] ) ;
Add(tables, t) ;
Add( SNLA_NAMES, "2457L" ) ;
t:= e( 7) ;
for i in [ 2, 3] do
s( t, 1, i, [ 1, i+ 1 ] ) ;
od ;
s( t, 1, 4, [ 1, 6 ] ) ;
s( t, 1, 5, [ 1, 7 ] ) ;
s( t, 2, 3, [ 1, 5 ] ) ;
s( t, 2, 4, [ 1, 7 ] ) ;
s( t, 2, 5, [ 1, 6 ] ) ;
Add(tables, t) ;
Add( SNLA_NAMES, "2457M" ) ;
t:= e( 7) ;
for i in [ 2, 3] do
s( t, 1, i, [ 1, i+ 1 ] ) ;
od ;
s( t, 1, 4, [ 1, 7 ] ) ;
s( t, 1, 5, [ 1, 6 ] ) ;
s( t, 2, 3, [ 1, 5 ] ) ;
s( t, 2, 4, [ 1, 6 ] ) ;
Add(tables, t) ;
## Upper Central Series Dimensions ( 2357)
Add( SNLA_NAMES, "2357A" ) ;
t:= e( 7) ;
s( t, 1, 2, [ 1, 4 ] ) ;
s( t, 1, 4, [ 1, 5 ] ) ;
s( t, 1, 5, [ 1, 7 ] ) ;
s( t, 2, 3, [ 1, 5, 1, 6 ] ) ;
s( t, 3, 4, [ - 1, 7 ] ) ;
Add(tables, t) ;
Add( SNLA_NAMES, "2357B" ) ;
t:= e( 7) ;
s( t, 1, 2, [ 1, 4 ] ) ;
s( t, 1, 3, [ 1, 6 ] ) ;
s( t, 1, 4, [ 1, 5 ] ) ;
s( t, 1, 5, [ 1, 7 ] ) ;
s( t, 2, 3, [ 1, 5 ] ) ;
s( t, 3, 4, [ - 1, 7 ] ) ;
Add(tables, t) ;
Add( SNLA_NAMES, "2357C" ) ;
t:= e( 7) ;
s( t, 1, 2, [ 1, 4 ] ) ;
s( t, 1, 4, [ 1, 5 ] ) ;
s( t, 1, 5, [ 1, 7 ] ) ;
s( t, 2, 3, [ 1, 5 ] ) ;
s( t, 2, 4, [ 1, 6 ] ) ;
s( t, 3, 4, [ - 1, 7 ] ) ;
Add(tables, t) ;
Add( SNLA_NAMES, "2357D" ) ;
t:= e( 7) ;
s( t, 1, 2, [ 1, 4 ] ) ;
s( t, 1, 3, [ 1, 6 ] ) ;
s( t, 1, 4, [ 1, 5 ] ) ;
s( t, 1, 5, [ 1, 7 ] ) ;
s( t, 2, 3, [ 1, 5 ] ) ;
s( t, 2, 4, [ 1, 6 ] ) ;
s( t, 3, 4, [ - 1, 7 ] ) ;
Add(tables, t) ;
## Upper Central Series Dimensions ( 23457)
Add( SNLA_NAMES, "23457A" ) ;
t:= e( 7) ;
for i in [ 2, 3, 4] do
s( t, 1, i, [ 1, i+ 1 ] ) ;
od ;
s( t, 1, 5, [ 1, 6 ] ) ;
s( t, 2, 3, [ 1, 7 ] ) ;
Add(tables, t) ;
Add( SNLA_NAMES, "23457B" ) ;
## Here another basis is used, with x_6 and x_7 swapped respect to the
## basis used by Gong
t:= e( 7) ;
for i in [ 2, 3, 4] do
s( t, 1, i, [ 1, i+ 1 ] ) ;
od ;
s( t, 2, 3, [ 1, 6 ] ) ;
s( t, 2, 5, [ 1, 7 ] ) ;
s( t, 3, 4, [ - 1, 7 ] ) ;
Add(tables, t) ;
Add( SNLA_NAMES, "23457C" ) ;
t:= e( 7) ;
for i in [ 2, 3, 4] do
s( t, 1, i, [ 1, i+ 1 ] ) ;
od ;
s( t, 1, 5, [ 1, 6 ] ) ;
s( t, 2, 5, [ 1, 7 ] ) ;
s( t, 3, 4, [ - 1, 7 ] ) ;
Add(tables, t) ;
Add( SNLA_NAMES, "23457D" ) ;
t:= e( 7) ;
for i in [ 2, 3, 4] do
s( t, 1, i, [ 1, i+ 1 ] ) ;
od ;
s( t, 1, 5, [ 1, 6 ] ) ;
s( t, 2, 3, [ 1, 6 ] ) ;
s( t, 2, 5, [ 1, 7 ] ) ;
s( t, 3, 4, [ - 1, 7 ] ) ;
Add(tables, t) ;
Add( SNLA_NAMES, "23457E" ) ;
t:= e( 7) ;
for i in [ 2, 3, 4] do
s( t, 1, i, [ 1, i+ 1 ] ) ;
od ;
s( t, 1, 5, [ 1, 6 ] ) ;
s( t, 2, 3, [ 1, 5, 1, 7 ] ) ;
s( t, 2, 4, [ 1, 6 ] ) ;
Add(tables, t) ;
Add( SNLA_NAMES, "23457F" ) ;
t:= e( 7) ;
for i in [ 2, 3, 4] do
s( t, 1, i, [ 1, i+ 1 ] ) ;
od ;
s( t, 2, 3, [ 1, 5, 1, 7 ] ) ;
s( t, 2, 5, [ 1, 6 ] ) ;
s( t, 3, 4, [ - 1, 6 ] ) ;
Add(tables, t) ;
Add( SNLA_NAMES, "23457G" ) ;
t:= e( 7) ;
for i in [ 2, 3, 4] do
s( t, 1, i, [ 1, i+ 1 ] ) ;
od ;
s( t, 1, 5, [ 1, 6 ] ) ;
s( t, 2, 3, [ 1, 5 ] ) ;
s( t, 2, 4, [ 1, 6 ] ) ;
s( t, 2, 5, [ 1, 7 ] ) ;
s( t, 3, 4, [ - 1, 7 ] ) ;
Add(tables, t) ;
## Upper Central Series Dimensions ( 17)
Add( SNLA_NAMES, "17" ) ;
t:= e( 7) ;
s( t, 1, 2, [ 1, 7 ] ) ;
s( t, 3, 4, [ 1, 7 ] ) ;
s( t, 5, 6, [ 1, 7 ] ) ;
Add(tables, t) ;
## Upper Central Series Dimensions ( 157)
Add( SNLA_NAMES, "157" ) ;
t:= e( 7) ;
s( t, 1, 2, [ 1, 3 ] ) ;
s( t, 1, 3, [ 1, 7 ] ) ;
s( t, 2, 4, [ 1, 7 ] ) ;
s( t, 5, 6, [ 1, 7 ] ) ;
Add(tables, t) ;
## Upper Central Series Dimensions ( 147)
Add( SNLA_NAMES, "147A" ) ;
t:= e( 7) ;
s( t, 1, 2, [ 1, 4 ] ) ;
s( t, 1, 3, [ 1, 5 ] ) ;
s( t, 1, 6, [ 1, 7 ] ) ;
s( t, 2, 5, [ 1, 7 ] ) ;
s( t, 3, 4, [ 1, 7 ] ) ;
Add(tables, t) ;
Add( SNLA_NAMES, "147B" ) ;
t:= e( 7) ;
s( t, 1, 2, [ 1, 4 ] ) ;
s( t, 1, 3, [ 1, 5 ] ) ;
s( t, 1, 4, [ 1, 7 ] ) ;
s( t, 2, 6, [ 1, 7 ] ) ;
s( t, 3, 5, [ 1, 7 ] ) ;
Add(tables, t) ;
if char<> 2 then
Add( SNLA_NAMES, "147C" ) ;
## It is a member of the one parameter family "147E", with
## lambda = - 1, 1/ 2, 2, and was not included by Gong, but this algebra has
## different invariants
t:= e( 7) ;
s( t, 1, 2, [ 1, 4 ] ) ;
s( t, 1, 3, [ - 1, 6 ] ) ;
s( t, 1, 5, [ - 1, 7 ] ) ;
s( t, 2, 3, [ 1, 5 ] ) ;
s( t, 2, 6, [ 1/ 2, 7 ] ) ;
s( t, 3, 4, [ 1/ 2, 7 ] ) ;
Add(tables, t) ;
fi ;
Add( SNLA_NAMES, "147D" ) ;
t:= e( 7) ;
s( t, 1, 2, [ 1, 4 ] ) ;
s( t, 1, 3, [ - 1, 6 ] ) ;
s( t, 1, 5, [ 1, 7 ] ) ;
s( t, 1, 6, [ 1, 7 ] ) ;
s( t, 2, 3, [ 1, 5 ] ) ;
s( t, 2, 6, [ 1, 7 ] ) ;
s( t, 3, 4, [ - 2, 7 ] ) ;
Add(tables, t) ;
Add( SNLA_NAMES, "147E" ) ;
## One parameter family, with invariant
## I( lambda) = ( 1 - lambda + lambda^ 2)^ 3 / ( lambda^ 2 ( lambda - 1)^ 2 ) ,
## lambda <> 0, 1.
t:= e( 7) ;
s( t, 1, 2, [ 1, 4 ] ) ;
s( t, 1, 3, [ - 1, 6 ] ) ;
s( t, 1, 5, [ - 1, 7 ] ) ;
s( t, 2, 3, [ 1, 5 ] ) ;
s( t, 2, 6, [ lambda, 7 ] ) ;
s( t, 3, 4, [ ( 1 - lambda), 7 ] ) ;
Add(tables, t) ;
## When lambda = 0 or 1, it is isomorphic to ( 247P).
if char= 3 then
Add( SNLA_NAMES, "147F" ) ;
## (for char = 3 only)
t:= e( 7) ;
s( t, 1, 2, [ 1, 4 ] ) ;
s( t, 1, 3, [ - 1, 6 ] ) ;
s( t, 1, 5, [ 1, 7 ] ) ;
s( t, 1, 6, [ 1, 7 ] ) ;
s( t, 2, 3, [ 1, 5 ] ) ;
s( t, 2, 4, [ 1, 7 ] ) ;
s( t, 2, 6, [ 1, 7 ] ) ;
s( t, 3, 4, [ 1, 7 ] ) ;
Add(tables, t) ;
fi ;
## Remark: ( 147C) in Seeley 's list is a special case of (147E) by taking
## lambda = 1.
## This is an error: it should be "lambda = -1, 1/2, 2".
## Upper Central Series Dimensions ( 1457)
Add( SNLA_NAMES, "1457A" ) ;
t:= e( 7) ;
for i in [ 2, 3] do
s( t, 1, i, [ 1, i+ 1 ] ) ;
od ;
s( t, 1, 4, [ 1, 7 ] ) ;
s( t, 5, 6, [ 1, 7 ] ) ;
Add(tables, t) ;
Add( SNLA_NAMES, "1457B" ) ;
t:= e( 7) ;
for i in [ 2, 3] do
s( t, 1, i, [ 1, i+ 1 ] ) ;
od ;
s( t, 1, 4, [ 1, 7 ] ) ;
s( t, 2, 3, [ 1, 7 ] ) ;
s( t, 5, 6, [ 1, 7 ] ) ;
Add(tables, t) ;
## Upper Central Series Dimensions ( 137)
Add( SNLA_NAMES, "137A" ) ;
t:= e( 7) ;
s( t, 1, 2, [ 1, 5 ] ) ;
s( t, 1, 5, [ 1, 7 ] ) ;
s( t, 3, 4, [ 1, 6 ] ) ;
s( t, 3, 6, [ 1, 7 ] ) ;
Add(tables, t) ;
Add( SNLA_NAMES, "137B" ) ;
t:= e( 7) ;
s( t, 1, 2, [ 1, 5 ] ) ;
s( t, 1, 5, [ 1, 7 ] ) ;
s( t, 2, 4, [ 1, 7 ] ) ;
s( t, 3, 4, [ 1, 6 ] ) ;
s( t, 3, 6, [ 1, 7 ] ) ;
Add(tables, t) ;
Add( SNLA_NAMES, "137C" ) ;
t:= e( 7) ;
s( t, 1, 2, [ 1, 5 ] ) ;
s( t, 1, 4, [ 1, 6 ] ) ;
s( t, 1, 6, [ 1, 7 ] ) ;
s( t, 2, 3, [ 1, 6 ] ) ;
s( t, 3, 5, [ - 1, 7 ] ) ;
Add(tables, t) ;
Add( SNLA_NAMES, "137D" ) ;
t:= e( 7) ;
s( t, 1, 2, [ 1, 5 ] ) ;
s( t, 1, 4, [ 1, 6 ] ) ;
s( t, 1, 6, [ 1, 7 ] ) ;
s( t, 2, 3, [ 1, 6 ] ) ;
s( t, 2, 4, [ 1, 7 ] ) ;
s( t, 3, 5, [ - 1, 7 ] ) ;
Add(tables, t) ;
## Upper Central Series Dimensions ( 1357)
Add( SNLA_NAMES, "1357A" ) ;
t:= e( 7) ;
s( t, 1, 2, [ 1, 4 ] ) ;
s( t, 1, 4, [ 1, 5 ] ) ;
s( t, 1, 5, [ 1, 7 ] ) ;
s( t, 2, 3, [ 1, 5 ] ) ;
s( t, 2, 6, [ 1, 7 ] ) ;
s( t, 3, 4, [ - 1, 7 ] ) ;
Add(tables, t) ;
Add( SNLA_NAMES, "1357B" ) ;
t:= e( 7) ;
s( t, 1, 2, [ 1, 4 ] ) ;
s( t, 1, 4, [ 1, 5 ] ) ;
s( t, 1, 5, [ 1, 7 ] ) ;
s( t, 2, 3, [ 1, 5 ] ) ;
s( t, 3, 4, [ - 1, 7 ] ) ;
s( t, 3, 6, [ 1, 7 ] ) ;
Add(tables, t) ;
Add( SNLA_NAMES, "1357C" ) ;
t:= e( 7) ;
s( t, 1, 2, [ 1, 4 ] ) ;
s( t, 1, 4, [ 1, 5 ] ) ;
s( t, 1, 5, [ 1, 7 ] ) ;
s( t, 2, 3, [ 1, 5 ] ) ;
s( t, 2, 4, [ 1, 7 ] ) ;
s( t, 3, 4, [ - 1, 7 ] ) ;
s( t, 3, 6, [ 1, 7 ] ) ;
Add(tables, t) ;
Add( SNLA_NAMES, "1357D" ) ;
t:= e( 7) ;
s( t, 1, 2, [ 1, 3 ] ) ;
s( t, 1, 6, [ 1, 7 ] ) ;
for i in [ 3, 4] do
s( t, 2, i, [ 1, i+ 2 ] ) ;
od ;
s( t, 2, 5, [ 1, 7 ] ) ;
s( t, 3, 4, [ 1, 7 ] ) ;
Add(tables, t) ;
Add( SNLA_NAMES, "1357E" ) ;
t:= e( 7) ;
s( t, 1, 2, [ 1, 3 ] ) ;
for i in [ 3, 4] do
s( t, 2, i, [ 1, i+ 2 ] ) ;
od ;
s( t, 2, 5, [ 1, 7 ] ) ;
s( t, 4, 6, [ 1, 7 ] ) ;
Add(tables, t) ;
Add( SNLA_NAMES, "1357F" ) ;
t:= e( 7) ;
s( t, 1, 2, [ 1, 3 ] ) ;
s( t, 1, 3, [ 1, 7 ] ) ;
for i in [ 3, 4] do
s( t, 2, i, [ 1, i+ 2 ] ) ;
od ;
s( t, 2, 5, [ 1, 7 ] ) ;
s( t, 4, 6, [ - 1, 7 ] ) ;
Add(tables, t) ;
Add( SNLA_NAMES, "1357G" ) ;
t:= e( 7) ;
s( t, 1, 2, [ 1, 3 ] ) ;
s( t, 1, 4, [ 1, 6 ] ) ;
s( t, 1, 6, [ 1, 7 ] ) ;
s( t, 2, 3, [ 1, 5 ] ) ;
s( t, 2, 5, [ 1, 7 ] ) ;
Add(tables, t) ;
Add( SNLA_NAMES, "1357H" ) ;
t:= e( 7) ;
s( t, 1, 2, [ 1, 3 ] ) ;
s( t, 1, 4, [ 1, 6 ] ) ;
s( t, 1, 6, [ 1, 7 ] ) ;
s( t, 2, 3, [ 1, 5 ] ) ;
s( t, 2, 5, [ 1, 7 ] ) ;
s( t, 2, 6, [ 1, 7 ] ) ;
s( t, 3, 4, [ - 1, 7 ] ) ;
Add(tables, t) ;
Add( SNLA_NAMES, "1357I" ) ;
t:= e( 7) ;
s( t, 1, 2, [ 1, 3 ] ) ;
s( t, 1, 4, [ 1, 6 ] ) ;
s( t, 2, 3, [ 1, 5 ] ) ;
s( t, 2, 5, [ 1, 7 ] ) ;
s( t, 4, 6, [ 1, 7 ] ) ;
Add(tables, t) ;
Add( SNLA_NAMES, "1357J" ) ;
t:= e( 7) ;
s( t, 1, 2, [ 1, 3 ] ) ;
s( t, 1, 3, [ 1, 7 ] ) ;
s( t, 1, 4, [ 1, 6 ] ) ;
s( t, 2, 3, [ 1, 5 ] ) ;
s( t, 2, 5, [ 1, 7 ] ) ;
s( t, 4, 6, [ 1, 7 ] ) ;
Add(tables, t) ;
if char<> 2 then
Add( SNLA_NAMES, "1357K" ) ;
## It is a member of the one parameter family "1357M", with
## lambda = 1/ 2, and was not included by Gong, but this algebra has
## different invariants
t:= e( 7) ;
s( t, 1, 2, [ 1, 3 ] ) ;
for i in [ 3, 4, 5] do
s( t, 1, i, [ 1, i+ 2 ] ) ;
od ;
s( t, 2, 4, [ 1, 5 ] ) ;
s( t, 2, 6, [ 1/ 2, 7 ] ) ;
s( t, 3, 4, [ 1/ 2, 7 ] ) ;
Add(tables, t) ;
fi ;
if char<> 2 then
Add( SNLA_NAMES, "1357L" ) ;
t:= e( 7) ;
s( t, 1, 2, [ 1, 3 ] ) ;
for i in [ 3, 4, 5] do
s( t, 1, i, [ 1, i+ 2 ] ) ;
od ;
s( t, 2, 3, [ 1, 7 ] ) ;
s( t, 2, 4, [ 1, 5 ] ) ;
s( t, 2, 6, [ 1/ 2, 7 ] ) ;
s( t, 3, 4, [ 1/ 2, 7 ] ) ;
Add(tables, t) ;
fi ;
Add( SNLA_NAMES, "1357M" ) ;
## One parameter family, with lambda <> 0
t:= e( 7) ;
s( t, 1, 2, [ 1, 3 ] ) ;
for i in [ 3, 4, 5] do
s( t, 1, i, [ 1, i+ 2 ] ) ;
od ;
s( t, 2, 4, [ 1, 5 ] ) ;
s( t, 2, 6, [ lambda, 7 ] ) ;
s( t, 3, 4, [ ( 1 - lambda), 7 ] ) ;
Add(tables, t) ;
## When lambda = 0, it is isomorphic to ( 2357B).
Add( SNLA_NAMES, "1357N" ) ;
## One parameter family.
t:= e( 7) ;
s( t, 1, 2, [ 1, 3 ] ) ;
for i in [ 3, 4, 5] do
s( t, 1, i, [ 1, i+ 2 ] ) ;
od ;
s( t, 2, 3, [ lambda, 7 ] ) ;
s( t, 2, 4, [ 1, 5 ] ) ;
s( t, 3, 4, [ 1, 7 ] ) ;
s( t, 4, 6, [ 1, 7 ] ) ;
Add(tables, t) ;
Add( SNLA_NAMES, "1357O" ) ;
t:= e( 7) ;
s( t, 1, 2, [ 1, 3 ] ) ;
s( t, 1, 3, [ 1, 5 ] ) ;
s( t, 1, 6, [ 1, 7 ] ) ;
s( t, 2, 3, [ 1, 6 ] ) ;
s( t, 2, 4, [ 1, 5 ] ) ;
s( t, 2, 5, [ 1, 7 ] ) ;
Add(tables, t) ;
Add( SNLA_NAMES, "1357P" ) ;
t:= e( 7) ;
s( t, 1, 2, [ 1, 3 ] ) ;
for i in [ 3, 5] do
s( t, 1, i, [ 1, i+ 2 ] ) ;
od ;
s( t, 2, 3, [ 1, 6 ] ) ;
s( t, 2, 4, [ 1, 5 ] ) ;
s( t, 2, 6, [ 1, 7 ] ) ;
s( t, 3, 4, [ 1, 7 ] ) ;
Add(tables, t) ;
Add( SNLA_NAMES, "1357Q" ) ;
t:= e( 7) ;
s( t, 1, 2, [ 1, 3 ] ) ;
s( t, 1, 3, [ 1, 5 ] ) ;
s( t, 1, 5, [ 1, 7 ] ) ;
s( t, 2, 3, [ 1, 6 ] ) ;
s( t, 2, 4, [ 1, 6 ] ) ;
s( t, 2, 6, [ 1, 7 ] ) ;
Add(tables, t) ;
Add( SNLA_NAMES, "1357R" ) ;
t:= e( 7) ;
s( t, 1, 2, [ 1, 3 ] ) ;
s( t, 1, 3, [ 1, 5 ] ) ;
s( t, 1, 6, [ 1, 7 ] ) ;
s( t, 2, 3, [ 1, 6 ] ) ;
s( t, 2, 4, [ 1, 6 ] ) ;
s( t, 2, 5, [ 1, 7 ] ) ;
s( t, 3, 4, [ 1, 7 ] ) ;
Add(tables, t) ;
Add( SNLA_NAMES, "1357S" ) ;
## One parameter family, with lambda <> 1
t:= e( 7) ;
s( t, 1, 2, [ 1, 3 ] ) ;
s( t, 1, 3, [ 1, 5 ] ) ;
s( t, 1, 5, [ 1, 7 ] ) ;
s( t, 1, 6, [ 1, 7 ] ) ;
s( t, 2, 3, [ 1, 6 ] ) ;
s( t, 2, 4, [ 1, 6 ] ) ;
s( t, 2, 5, [ 1, 7 ] ) ;
s( t, 2, 6, [ lambda, 7 ] ) ;
s( t, 3, 4, [ 1, 7 ] ) ;
Add(tables, t) ;
## When lambda = 1, it is isomorphic to ( 2357D).
## Remark: ( 1357K) in Seeley 's list is a special case of
## ( 1357M) by taking lambda = 1/ 2:
## Upper Central Series Dimensions ( 13457)
Add( SNLA_NAMES, "13457A" ) ;
t:= e( 7) ;
for i in [ 2, 3, 4] do
s( t, 1, i, [ 1, i+ 1 ] ) ;
od ;
s( t, 1, 5, [ 1, 7 ] ) ;
s( t, 2, 6, [ 1, 7 ] ) ;
Add(tables, t) ;
Add( SNLA_NAMES, "13457B" ) ;
t:= e( 7) ;
for i in [ 2, 3, 4] do
s( t, 1, i, [ 1, i+ 1 ] ) ;
od ;
s( t, 1, 5, [ 1, 7 ] ) ;
s( t, 2, 3, [ 1, 7 ] ) ;
s( t, 2, 6, [ 1, 7 ] ) ;
Add(tables, t) ;
Add( SNLA_NAMES, "13457C" ) ;
t:= e( 7) ;
for i in [ 2, 3, 4] do
s( t, 1, i, [ 1, i+ 1 ] ) ;
od ;
s( t, 1, 6, [ 1, 7 ] ) ;
s( t, 2, 5, [ 1, 7 ] ) ;
s( t, 3, 4, [ - 1, 7 ] ) ;
Add(tables, t) ;
Add( SNLA_NAMES, "13457D" ) ;
t:= e( 7) ;
for i in [ 2, 3, 4] do
s( t, 1, i, [ 1, i+ 1 ] ) ;
od ;
s( t, 1, 5, [ 1, 7 ] ) ;
s( t, 2, 3, [ 1, 5 ] ) ;
s( t, 2, 4, [ 1, 7 ] ) ;
s( t, 2, 6, [ 1, 7 ] ) ;
Add(tables, t) ;
Add( SNLA_NAMES, "13457E" ) ;
t:= e( 7) ;
for i in [ 2, 3, 4] do
s( t, 1, i, [ 1, i+ 1 ] ) ;
od ;
s( t, 1, 6, [ 1, 7 ] ) ;
s( t, 2, 3, [ 1, 5 ] ) ;
s( t, 2, 5, [ 1, 7 ] ) ;
s( t, 3, 4, [ - 1, 7 ] ) ;
Add(tables, t) ;
Add( SNLA_NAMES, "13457F" ) ;
t:= e( 7) ;
for i in [ 2, 3, 4] do
s( t, 1, i, [ 1, i+ 1 ] ) ;
od ;
s( t, 1, 5, [ 1, 7 ] ) ;
s( t, 2, 3, [ 1, 6 ] ) ;
s( t, 2, 6, [ 1, 7 ] ) ;
Add(tables, t) ;
Add( SNLA_NAMES, "13457G" ) ;
t:= e( 7) ;
for i in [ 2, 3, 4] do
s( t, 1, i, [ 1, i+ 1 ] ) ;
od ;
s( t, 1, 6, [ 1, 7 ] ) ;
s( t, 2, 3, [ 1, 6 ] ) ;
s( t, 2, 4, [ 1, 7 ] ) ;
s( t, 2, 5, [ 1, 7 ] ) ;
s( t, 3, 4, [ - 1, 7 ] ) ;
Add(tables, t) ;
Add( SNLA_NAMES, "13457I" ) ;
t:= e( 7) ;
for i in [ 2, 3, 4] do
s( t, 1, i, [ 1, i+ 1 ] ) ;
od ;
s( t, 1, 5, [ 1, 7 ] ) ;
s( t, 2, 3, [ 1, 6 ] ) ;
s( t, 2, 5, [ 1, 7 ] ) ;
s( t, 2, 6, [ 1, 7 ] ) ;
s( t, 3, 4, [ - 1, 7 ] ) ;
Add(tables, t) ;
## Remark: ( 13457H) in Seeley 's list is not a Lie algebra, should be
## deleted.
## Upper Central Series Dimensions ( 12457)
Add( SNLA_NAMES, "12457A" ) ;
t:= e( 7) ;
for i in [ 2, 3] do
s( t, 1, i, [ 1, i+ 1 ] ) ;
od ;
s( t, 1, 4, [ 1, 6 ] ) ;
s( t, 1, 6, [ 1, 7 ] ) ;
s( t, 2, 5, [ 1, 6 ] ) ;
s( t, 3, 5, [ 1, 7 ] ) ;
Add(tables, t) ;
Add( SNLA_NAMES, "12457B" ) ;
t:= e( 7) ;
for i in [ 2, 3] do
s( t, 1, i, [ 1, i+ 1 ] ) ;
od ;
s( t, 1, 4, [ 1, 6 ] ) ;
s( t, 1, 6, [ 1, 7 ] ) ;
s( t, 2, 5, [ 1, 6, 1, 7 ] ) ;
s( t, 3, 5, [ 1, 7 ] ) ;
Add(tables, t) ;
Add( SNLA_NAMES, "12457C" ) ;
t:= e( 7) ;
for i in [ 2, 3] do
s( t, 1, i, [ 1, i+ 1 ] ) ;
od ;
s( t, 1, 4, [ 1, 6 ] ) ;
s( t, 2, 5, [ 1, 6 ] ) ;
s( t, 2, 6, [ 1, 7 ] ) ;
s( t, 3, 4, [ - 1, 7 ] ) ;
Add(tables, t) ;
Add( SNLA_NAMES, "12457D" ) ;
t:= e( 7) ;
for i in [ 2, 3] do
s( t, 1, i, [ 1, i+ 1 ] ) ;
od ;
for i in [ 4, 5] do
s( t, 1, i, [ 1, i+ 2 ] ) ;
od ;
s( t, 2, 5, [ 1, 6 ] ) ;
s( t, 2, 6, [ 1, 7 ] ) ;
s( t, 3, 4, [ - 1, 7 ] ) ;
Add(tables, t) ;
Add( SNLA_NAMES, "12457E" ) ;
t:= e( 7) ;
for i in [ 2, 3] do
s( t, 1, i, [ 1, i+ 1 ] ) ;
od ;
s( t, 1, 4, [ 1, 6 ] ) ;
s( t, 1, 6, [ 1, 7 ] ) ;
s( t, 2, 3, [ 1, 6 ] ) ;
s( t, 2, 4, [ 1, 7 ] ) ;
s( t, 2, 5, [ 1, 6 ] ) ;
s( t, 3, 5, [ 1, 7 ] ) ;
Add(tables, t) ;
Add( SNLA_NAMES, "12457F" ) ;
t:= e( 7) ;
for i in [ 2, 3] do
s( t, 1, i, [ 1, i+ 1 ] ) ;
od ;
s( t, 1, 4, [ 1, 6 ] ) ;
s( t, 2, 3, [ 1, 6 ] ) ;
for i in [ 5, 6] do
s( t, 2, i, [ 1, i+ 1 ] ) ;
od ;
s( t, 3, 4, [ - 1, 7 ] ) ;
Add(tables, t) ;
Add( SNLA_NAMES, "12457G" ) ;
t:= e( 7) ;
for i in [ 2, 3] do
s( t, 1, i, [ 1, i+ 1 ] ) ;
od ;
s( t, 1, 4, [ 1, 6 ] ) ;
s( t, 1, 5, [ 1, 7 ] ) ;
s( t, 2, 3, [ 1, 6 ] ) ;
for i in [ 5, 6] do
s( t, 2, i, [ 1, i+ 1 ] ) ;
od ;
s( t, 3, 4, [ - 1, 7 ] ) ;
Add(tables, t) ;
Add( SNLA_NAMES, "12457H" ) ;
t:= e( 7) ;
for i in [ 2, 3, 5, 6] do
s( t, 1, i, [ 1, i+ 1 ] ) ;
od ;
for j in [ 3, 4] do
s( t, 2, j, [ 1, j+ 2 ] ) ;
od ;
s( t, 3, 4, [ 1, 7 ] ) ;
Add(tables, t) ;
Add( SNLA_NAMES, "12457I" ) ;
t:= e( 7) ;
for i in [ 2, 3, 5, 6] do
s( t, 1, i, [ 1, i+ 1 ] ) ;
od ;
for j in [ 3, 4] do
s( t, 2, j, [ 1, j+ 2 ] ) ;
od ;
s( t, 2, 5, [ 1, 7 ] ) ;
s( t, 3, 4, [ 1, 7 ] ) ;
Add(tables, t) ;
Add( SNLA_NAMES, "12457J" ) ;
t:= e( 7) ;
for i in [ 2, 3, 5, 6] do
s( t, 1, i, [ 1, i+ 1 ] ) ;
od ;
s( t, 1, 4, [ 1, 7 ] ) ;
s( t, 2, 3, [ 1, 5 ] ) ;
s( t, 2, 4, [ 1, 6 ] ) ;
s( t, 2, 5, [ 1, 7 ] ) ;
s( t, 3, 4, [ 1, 7 ] ) ;
Add(tables, t) ;
Add( SNLA_NAMES, "12457K" ) ;
t:= e( 7) ;
for i in [ 2, 3, 5, 6] do
s( t, 1, i, [ 1, i+ 1 ] ) ;
od ;
s( t, 1, 4, [ 1, 7 ] ) ;
s( t, 2, 3, [ 1, 5 ] ) ;
s( t, 2, 4, [ 1, 6 ] ) ;
s( t, 3, 4, [ 1, 7 ] ) ;
Add(tables, t) ;
Add( SNLA_NAMES, "12457L" ) ;
t:= e( 7) ;
for i in [ 2, 3, 5, 6] do
s( t, 1, i, [ 1, i+ 1 ] ) ;
od ;
for j in [ 3, 4] do
s( t, 2, j, [ 1, j+ 2 ] ) ;
od ;
s( t, 2, 6, [ 1, 7 ] ) ;
s( t, 3, 4, [ 1, 7 ] ) ;
s( t, 3, 5, [ - 1, 7 ] ) ;
Add(tables, t) ;
Add( SNLA_NAMES, "12457N" ) ;
## One parameter family, with invariant I( lambda) = lambda + lambda^- 1.
t:= e( 7) ;
for i in [ 2, 3, 5, 6] do
s( t, 1, i, [ 1, i+ 1 ] ) ;
od ;
s( t, 1, 4, [ 1, 7 ] ) ;
s( t, 2, 3, [ 1, 5 ] ) ;
s( t, 2, 4, [ 1, 6 ] ) ;
s( t, 2, 5, [ lambda, 7 ] ) ;
s( t, 2, 6, [ 1, 7 ] ) ;
s( t, 3, 4, [ 1, 7 ] ) ;
s( t, 3, 5, [ - 1, 7 ] ) ;
Add(tables, t) ;
## Remark: ( 12457M) in Seeley 's list is just a special case of
## ( 12457N) by taking lambda = 0.
## Upper Central Series Dimensions ( 12357)
Add( SNLA_NAMES, "12357A" ) ;
t:= e( 7) ;
s( t, 1, 2, [ 1, 4 ] ) ;
for i in [ 4, 5, 6] do
s( t, 1, i, [ 1, i+ 1 ] ) ;
od ;
s( t, 2, 3, [ 1, 5 ] ) ;
s( t, 3, 4, [ - 1, 6 ] ) ;
s( t, 3, 5, [ - 1, 7 ] ) ;
Add(tables, t) ;
Add( SNLA_NAMES, "12357B" ) ;
t:= e( 7) ;
s( t, 1, 2, [ 1, 4 ] ) ;
for i in [ 4, 5, 6] do
s( t, 1, i, [ 1, i+ 1 ] ) ;
od ;
s( t, 2, 3, [ 1, 5, 1, 7 ] ) ;
s( t, 3, 4, [ - 1, 6 ] ) ;
s( t, 3, 5, [ - 1, 7 ] ) ;
Add(tables, t) ;
Add( SNLA_NAMES, "12357C" ) ;
t:= e( 7) ;
s( t, 1, 2, [ 1, 4 ] ) ;
for i in [ 4, 5, 6] do
s( t, 1, i, [ 1, i+ 1 ] ) ;
od ;
s( t, 2, 3, [ 1, 5 ] ) ;
s( t, 2, 4, [ 1, 7 ] ) ;
s( t, 3, 4, [ - 1, 6 ] ) ;
s( t, 3, 5, [ - 1, 7 ] ) ;
Add(tables, t) ;
## Upper Central Series Dimensions ( 123457)
Add( SNLA_NAMES, "123457A" ) ;
t:= e( 7) ;
for i in [ 2 .. 6] do
s( t, 1, i, [ 1, i+ 1 ] ) ;
od ;
Add(tables, t) ;
Add( SNLA_NAMES, "123457B" ) ;
t:= e( 7) ;
for i in [ 2 .. 6] do
s( t, 1, i, [ 1, i+ 1 ] ) ;
od ;
s( t, 2, 3, [ 1, 7 ] ) ;
Add(tables, t) ;
Add( SNLA_NAMES, "123457C" ) ;
t:= e( 7) ;
for i in [ 2 .. 6] do
s( t, 1, i, [ 1, i+ 1 ] ) ;
od ;
s( t, 2, 5, [ 1, 7 ] ) ;
s( t, 3, 4, [ - 1, 7 ] ) ;
Add(tables, t) ;
Add( SNLA_NAMES, "123457D" ) ;
t:= e( 7) ;
for i in [ 2 .. 5] do
s( t, 1, i, [ 1, i+ 1 ] ) ;
od ;
s( t, 1, 6, [ 1, 7 ] ) ;
s( t, 2, 3, [ 1, 6 ] ) ;
s( t, 2, 4, [ 1, 7 ] ) ;
Add(tables, t) ;
Add( SNLA_NAMES, "123457E" ) ;
t:= e( 7) ;
for i in [ 2 .. 5] do
s( t, 1, i, [ 1, i+ 1 ] ) ;
od ;
s( t, 1, 6, [ 1, 7 ] ) ;
s( t, 2, 3, [ 1, 6, 1, 7 ] ) ;
s( t, 2, 4, [ 1, 7 ] ) ;
Add(tables, t) ;
Add( SNLA_NAMES, "123457F" ) ;
t:= e( 7) ;
for i in [ 2 .. 5] do
s( t, 1, i, [ 1, i+ 1 ] ) ;
od ;
s( t, 1, 6, [ 1, 7 ] ) ;
s( t, 2, 3, [ 1, 6 ] ) ;
s( t, 2, 4, [ 1, 7 ] ) ;
s( t, 2, 5, [ 1, 7 ] ) ;
s( t, 3, 4, [ - 1, 7 ] ) ;
Add(tables, t) ;
Add( SNLA_NAMES, "123457G" ) ;
## It is a member of the one parameter family "123457I", with
## lambda = 1, and was not included by Gong, but this algebra has
## different invariants
t:= e( 7) ;
for i in [ 2 .. 5] do
s( t, 1, i, [ 1, i+ 1 ] ) ;
od ;
s( t, 1, 6, [ 1, 7 ] ) ;
s( t, 2, 3, [ 1, 5 ] ) ;
s( t, 2, 4, [ 1, 6 ] ) ;
s( t, 2, 5, [ 1, 7 ] ) ;
Add(tables, t) ;
Add( SNLA_NAMES, "123457H" ) ;
t:= e( 7) ;
for i in [ 2 .. 5] do
s( t, 1, i, [ 1, i+ 1 ] ) ;
od ;
s( t, 1, 6, [ 1, 7 ] ) ;
s( t, 2, 3, [ 1, 5, 1, 7 ] ) ;
s( t, 2, 4, [ 1, 6 ] ) ;
s( t, 2, 5, [ 1, 7 ] ) ;
Add(tables, t) ;
Add( SNLA_NAMES, "123457I" ) ;
## One parameter family.
t:= e( 7) ;
for i in [ 2 .. 5] do
s( t, 1, i, [ 1, i+ 1 ] ) ;
od ;
s( t, 1, 6, [ 1, 7 ] ) ;
s( t, 2, 3, [ 1, 5 ] ) ;
s( t, 2, 4, [ 1, 6 ] ) ;
s( t, 2, 5, [ lambda, 7 ] ) ;
s( t, 3, 4, [ ( 1 - lambda), 7 ] ) ;
Add(tables, t) ;
## Remark: ( 123457G) in Seeley 's list is a special case of (123457I) with
## lambda = 1.
## Paragraph 4. 2
## List of 7-Dimensional Indecomposable Nilpotent Lie Algebras over the
## Real Field
## Each of the algebras in the list of Section 4. 1 can be interpreted as a
## Lie algebra over R. In the case of infinite families, we have to
## restrict the parameter lambda to take real values. The exceptional
## algebra which occurs in the case char = 3 should be omitted. In
## addition to these algebras, we have the following 24 extra
## indecomposable algebras over the real field R.
## Upper Central Series Dimensions ( 37)
Add( SNLA_NAMES, "37B1" ) ;
t:= e( 7) ;
s( t, 1, 2, [ 1, 5 ] ) ;
s( t, 1, 3, [ 1, 6 ] ) ;
s( t, 1, 4, [ 1, 7 ] ) ;
s( t, 2, 4, [ 1, 6 ] ) ;
s( t, 3, 4, [ - 1, 5 ] ) ;
Add(tables, t) ;
Add( SNLA_NAMES, "37D1" ) ;
t:= e( 7) ;
s( t, 1, 2, [ 1, 5 ] ) ;
s( t, 1, 3, [ 1, 6 ] ) ;
s( t, 1, 4, [ 1, 7 ] ) ;
s( t, 2, 3, [ - 1, 7 ] ) ;
s( t, 2, 4, [ 1, 6 ] ) ;
s( t, 3, 4, [ - 1, 5 ] ) ;
Add(tables, t) ;
## Upper Central Series Dimensions ( 257)
Add( SNLA_NAMES, "257J1" ) ;
t:= e( 7) ;
s( t, 1, 2, [ 1, 3 ] ) ;
s( t, 1, 3, [ 1, 6 ] ) ;
s( t, 1, 4, [ 1, 6 ] ) ;
s( t, 1, 5, [ 1, 7 ] ) ;
s( t, 2, 3, [ 1, 7 ] ) ;
s( t, 2, 5, [ 1, 6 ] ) ;
Add(tables, t) ;
## Upper Central Series Dimensions ( 247)
Add( SNLA_NAMES, "247E1" ) ;
t:= e( 7) ;
for i in [ 2, 3, 4] do
s( t, 1, i, [ 1, i+ 2 ] ) ;
od ;
s( t, 2, 4, [ 1, 7 ] ) ;
s( t, 3, 5, [ 1, 7 ] ) ;
Add(tables, t) ;
Add( SNLA_NAMES, "247F1" ) ;
t:= e( 7) ;
for i in [ 2, 3] do
s( t, 1, i, [ 1, i+ 2 ] ) ;
od ;
s( t, 2, 4, [ 1, 6 ] ) ;
s( t, 2, 5, [ 1, 7 ] ) ;
s( t, 3, 4, [ 1, 7 ] ) ;
s( t, 3, 5, [ - 1, 6 ] ) ;
Add(tables, t) ;
Add( SNLA_NAMES, "247H1" ) ;
t:= e( 7) ;
for i in [ 2, 3, 4] do
s( t, 1, i, [ 1, i+ 2 ] ) ;
od ;
s( t, 2, 4, [ 1, 6 ] ) ;
s( t, 2, 5, [ 1, 7 ] ) ;
s( t, 3, 4, [ 1, 7 ] ) ;
s( t, 3, 5, [ - 1, 6 ] ) ;
Add(tables, t) ;
Add( SNLA_NAMES, "247P1" ) ;
t:= e( 7) ;
for i in [ 2, 3] do
s( t, 1, i, [ 1, i+ 2 ] ) ;
od ;
s( t, 2, 3, [ 1, 6 ] ) ;
s( t, 2, 4, [ 1, 7 ] ) ;
s( t, 3, 5, [ 1, 7 ] ) ;
Add(tables, t) ;
Add( SNLA_NAMES, "247R1" ) ;
t:= e( 7) ;
for i in [ 2, 3, 4] do
s( t, 1, i, [ 1, i+ 2 ] ) ;
od ;
s( t, 2, 3, [ 1, 6 ] ) ;
s( t, 2, 4, [ 1, 7 ] ) ;
s( t, 3, 5, [ 1, 7 ] ) ;
Add(tables, t) ;
## Upper Central Series Dimensions ( 2457)
Add( SNLA_NAMES, "2457L1" ) ;
t:= e( 7) ;
for i in [ 2, 3] do
s( t, 1, i, [ 1, i+ 1 ] ) ;
od ;
s( t, 1, 4, [ 1, 6 ] ) ;
s( t, 1, 5, [ 1, 7 ] ) ;
s( t, 2, 3, [ 1, 5 ] ) ;
s( t, 2, 4, [ 1, 7 ] ) ;
s( t, 2, 5, [ - 1, 6 ] ) ;
Add(tables, t) ;
## Upper Central Series Dimensions ( 2357)
Add( SNLA_NAMES, "2357D1" ) ;
t:= e( 7) ;
s( t, 1, 2, [ 1, 4 ] ) ;
s( t, 1, 3, [ 1, 6 ] ) ;
s( t, 1, 4, [ 1, 5 ] ) ;
s( t, 1, 5, [ 1, 7 ] ) ;
s( t, 2, 3, [ 1, 5 ] ) ;
s( t, 2, 4, [ - 1, 6 ] ) ;
s( t, 3, 4, [ - 1, 7 ] ) ;
Add(tables, t) ;
## Upper Central Series Dimensions ( 147)
Add( SNLA_NAMES, "147A1" ) ;
t:= e( 7) ;
s( t, 1, 2, [ 1, 4 ] ) ;
s( t, 1, 3, [ 1, 5 ] ) ;
s( t, 1, 6, [ 1, 7 ] ) ;
s( t, 2, 4, [ 1, 7 ] ) ;
s( t, 3, 5, [ 1, 7 ] ) ;
Add(tables, t) ;
if char<> 2 then
Add( SNLA_NAMES, "147E1" ) ;
## One parameter family, with lambda > 1
t:= e( 7) ;
s( t, 1, 2, [ 1, 4 ] ) ;
s( t, 2, 3, [ 1, 5 ] ) ;
s( t, 1, 3, [ - 1, 6 ] ) ;
s( t, 1, 6, [ - lambda, 7 ] ) ;
s( t, 2, 5, [ lambda, 7 ] ) ;
s( t, 2, 6, [ 2, 7 ] ) ;
s( t, 3, 4, [ - 2, 7 ] ) ;
Add(tables, t) ;
fi ;
## Upper Central Series Dimensions ( 137)
Add( SNLA_NAMES, "137A1" ) ;
t:= e( 7) ;
s( t, 1, 3, [ 1, 5 ] ) ;
s( t, 1, 4, [ 1, 6 ] ) ;
s( t, 1, 5, [ 1, 7 ] ) ;
s( t, 2, 3, [ - 1, 6 ] ) ;
s( t, 2, 4, [ 1, 5 ] ) ;
s( t, 2, 6, [ 1, 7 ] ) ;
Add(tables, t) ;
Add( SNLA_NAMES, "137B1" ) ;
t:= e( 7) ;
s( t, 1, 3, [ 1, 5 ] ) ;
s( t, 1, 4, [ 1, 6 ] ) ;
s( t, 1, 5, [ 1, 7 ] ) ;
s( t, 2, 3, [ - 1, 6 ] ) ;
s( t, 2, 4, [ 1, 5 ] ) ;
s( t, 2, 6, [ 1, 7 ] ) ;
s( t, 3, 4, [ 1, 7 ] ) ;
Add(tables, t) ;
## Upper Central Series Dimensions ( 1357)
Add( SNLA_NAMES, "1357F1" ) ;
t:= e( 7) ;
s( t, 1, 2, [ 1, 3 ] ) ;
s( t, 1, 3, [ 1, 7 ] ) ;
for i in [ 3, 4] do
s( t, 2, i, [ 1, i+ 2 ] ) ;
od ;
s( t, 2, 5, [ 1, 7 ] ) ;
s( t, 4, 6, [ 1, 7 ] ) ;
Add(tables, t) ;
Add( SNLA_NAMES, "1357P1" ) ;
t:= e( 7) ;
s( t, 1, 2, [ 1, 3 ] ) ;
for i in [ 3, 5] do
s( t, 1, i, [ 1, i+ 2 ] ) ;
od ;
s( t, 2, 3, [ 1, 6 ] ) ;
s( t, 2, 4, [ 1, 5 ] ) ;
s( t, 2, 6, [ - 1, 7 ] ) ;
s( t, 3, 4, [ 1, 7 ] ) ;
Add(tables, t) ;
Add( SNLA_NAMES, "1357Q1" ) ;
t:= e( 7) ;
s( t, 1, 2, [ 1, 3 ] ) ;
s( t, 1, 3, [ 1, 5 ] ) ;
s( t, 1, 5, [ 1, 7 ] ) ;
s( t, 2, 3, [ 1, 6 ] ) ;
s( t, 2, 4, [ 1, 6 ] ) ;
s( t, 2, 6, [ - 1, 7 ] ) ;
Add(tables, t) ;
Add( SNLA_NAMES, "1357QRS1" ) ;
## One parameter family, with invariant I( lambda) = lambda + lambda^- 1 and
## lambda <> 0.
t:= e( 7) ;
s( t, 1, 2, [ 1, 3 ] ) ;
s( t, 1, 3, [ 1, 5 ] ) ;
s( t, 1, 4, [ 1, 6 ] ) ;
s( t, 1, 5, [ 1, 7 ] ) ;
s( t, 2, 3, [ - 1, 6] ) ;
s( t, 2, 4, [ 1, 5 ] ) ;
s( t, 2, 6, [ lambda, 7 ] ) ;
s( t, 3, 4, [ ( 1 - lambda), 7 ] ) ;
Add(tables, t) ;
## When lambda = 1, ( 1357QRS1), =~ ( 1357Q) over C ;
## When lambda = - 1, ( 1357QRS1) =~ ( 1357R) over C.
## ( 1357QRS1, lambda <> 0, 1, - 1 ) becomes ( 1357S, lambda > 1) over C.
## When lambda = 0, it becomes ( 2357D).
## Upper Central Series Dimensions ( 12457)
Add( SNLA_NAMES, "12457J1" ) ;
t:= e( 7) ;
for i in [ 2, 3, 5, 6] do
s( t, 1, i, [ 1, i+ 1 ] ) ;
od ;
s( t, 1, 4, [ 1, 7 ] ) ;
for j in [ 3, 4] do
s( t, 2, j, [ 1, j+ 2 ] ) ;
od ;
s( t, 2, 5, [ - 1, 7 ] ) ;
s( t, 3, 4, [ 1, 7 ] ) ;
Add(tables, t) ;
Add( SNLA_NAMES, "12457L1" ) ;
t:= e( 7) ;
for i in [ 2, 3] do
s( t, 1, i, [ 1, i+ 1 ] ) ;
od ;
s( t, 1, 4, [ - 1, 6 ] ) ;
s( t, 1, 6, [ 1, 7 ] ) ;
s( t, 2, 3, [ 1, 5 ] ) ;
s( t, 2, 5, [ - 1, 6 ] ) ;
s( t, 3, 5, [ - 1, 7 ] ) ;
Add(tables, t) ;
Add( SNLA_NAMES, "12457N1" ) ;
t:= e( 7) ;
for i in [ 2, 3] do
s( t, 1, i, [ 1, i+ 1 ] ) ;
od ;
s( t, 1, 4, [ - 1, 6 ] ) ;
s( t, 1, 6, [ 1, 7 ] ) ;
s( t, 2, 3, [ 1, 5 ] ) ;
s( t, 2, 5, [ - 1, 6, 1, 7 ] ) ;
s( t, 3, 5, [ - 1, 7 ] ) ;
Add(tables, t) ;
## It is isomorphic to ( 12457N, lambda = 1) over C.
Add( SNLA_NAMES, "12457N2" ) ;
## One parameter family, with lambda lambda >= 0.
t:= e( 7) ;
for i in [ 2, 3] do
s( t, 1, i, [ 1, i+ 1 ] ) ;
od ;
s( t, 1, 4, [ - 1, 6 ] ) ;
s( t, 1, 5, [ 1, 7 ] ) ;
s( t, 1, 6, [ 1, 7 ] ) ;
s( t, 2, 3, [ 1, 5 ] ) ;
s( t, 2, 4, [ 1, 7 ] ) ;
s( t, 2, 5, [ - 1, 6, lambda, 7 ] ) ;
s( t, 3, 5, [ - 1, 7 ] ) ;
Add(tables, t) ;
## It is isomorphic to ( 12457N, lambda <> 1) over C.
## Upper Central Series Dimensions ( 12357)
Add( SNLA_NAMES, "12357B1" ) ;
t:= e( 7) ;
s( t, 1, 2, [ 1, 4 ] ) ;
for i in [ 4, 5, 6] do
s( t, 1, i, [ 1, i+ 1 ] ) ;
od ;
s( t, 2, 3, [ 1, 5, - 1, 7 ] ) ;
s( t, 3, 4, [ - 1, 6 ] ) ;
s( t, 3, 5, [ - 1, 7 ] ) ;
Add(tables, t) ;
## Upper Central Series Dimensions ( 123457)
Add( SNLA_NAMES, "123457H1" ) ;
t:= e( 7) ;
for i in [ 2 .. 5] do
s( t, 1, i, [ 1, i+ 1 ] ) ;
od ;
s( t, 1, 6, [ - 1, 7 ] ) ;
s( t, 2, 3, [ 1, 5, 1, 7 ] ) ;
s( t, 2, 4, [ 1, 6 ] ) ;
s( t, 2, 5, [ - 1, 7 ] ) ;
Add(tables, t) ;
if not ForAll(tables, x-> TestJacobi(x)=true) then Error( "TestJacobi") ;fi;
l := List( tables, x -> LieAlgebraByStructureConstants( campo, x ) ) ;
for i in [ 1..Length(l)] do
SetSnLa_Name(l[i], SNLA_NAMES[i]) ;
od ;
return l ;
end ) ;
[Dauer der Verarbeitung: 0.23 Sekunden, vorverarbeitet 2026-10-28]
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2026-11-01
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