| Quellcodebibliothek Statistik Leitseite products/Sources/formale Sprachen/GAP/pkg/corelg/gap/ (GAP Algebra Version 4.15.1©) Datei vom 7.6.2024 mit Größe 2 kB |
|
Quelle carrierrtsys.gd Sprache: Shell |
|||||||||||||||||||||||||
|
############################################################################## ## #F RootsystemOfCartanSubalgebra( <L> ) #F RootsystemOfCartanSubalgebra( <L>, <H> ) ## ## <L> is a semisimple lie algebra over Gaussian rationals or SqrtField; ## this function returns a rootsystem of <L> with respect to <H>, and ## with repect to CartanSubalgebra(<L>) if <H> is not provided ## DeclareGlobalFunction( "RootsystemOfCartanSubalgebra" ); ############################################################################## ## #F RootSystemOfZGradedLieAlgebra( <L>, <gr> ); #F RootSystemOfZGradedLieAlgebra( <L>, <gr>, <H> ); ## ## <L> is a semisimple lie algebra over Gaussian rationals or SqrtField ## with Z-grading <gr>, which is a record with entries g0, gp, gn; ## this function returns a rootsystem of <L> with respect to <H>, and ## with repect to CartanSubalgebra(<L>) if <H> is not provided, such that ## the simple roots lie in <gr>.gp[1] and <gr>.g0 ## DeclareGlobalFunction( "RootSystemOfZGradedLieAlgebra" ); ############################################################################## ## #F LieAlgebraIsomorphismByCanonicalGenerators( <L1>, <R1>, <L2>, <R2> ) ## ## <L1> and <L2> both are semisimple lie algebras over Gaussian rationals or SqrtField ## and either <R1> and <R2> both are canonical generators of <L1> and <L2> defining ## the same Cartan Matrix, of <R1> and <R2> are rootsystems or Cartan subalgebras of ## <L1> and <L2>, respectively; this functions constructs an isomorphism from ## <L1> to <L2> by mapping canonical generators onto canonical generators. ## Attention: This function does not check whether the map actually is a ## Lie isomorphisms! ## DeclareGlobalFunction( "LieAlgebraIsomorphismByCanonicalGenerators" ); ############################################################################## ## #F RegularCarrierAlgebraOfSL2Triple( <L>, <sl2> ) ## ## <L> is a semisimple lie algebra over Gaussian rationals or SqrtField ## and <sl2> is an SL2-triple in <L> of the form [f,h,e] with ef=h, he=2e, hf=-2f; ## this function returns the Z-graded carrier algebra of <sl2> normalised by ## CartanSubalgebra(<L>). ## DeclareGlobalFunction( "RegularCarrierAlgebraOfSL2Triple" ); ############################################################################## ## #A ChevalleyBasis( <R> ) # DeclareAttribute( "ChevalleyBasis", IsRootSystem ); ############################################################################## ## #P IsIsomorphismOfLieAlgebras( <iso> ) # DeclareProperty( "IsIsomorphismOfLieAlgebras", IsAlgebraHomomorphism );
¤ Dauer der Verarbeitung: 0.2 Sekunden ¤*© Formatika GbR, Deutschland |
|
||||||||||||||||||||||||
2026-11-04