<?xml version="1.0" encoding="UTF-8" ?>DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd " >html xmlns="http://www.w3.org/1999/xhtml " xml:lang="en" >head >title >GAP (LieAlgDB) - Contents</title >meta http-equiv="content-type" content="text/html; charset=UTF-8" />meta name="generator" content="GAPDoc2HTML" />link rel="stylesheet" type="text/css" href="manual.css" />script src="manual.js" type="text/javascript" ></script >script type="text/javascript" >overwriteStyle();</script >head >body class="chap0" onload="jscontent()" >div class="chlinktop" ><span class="chlink1" >Goto Chapter: </span ><a href="chap0.html" >Top</a> <a href="chap1.html" >1</a> <a href="chap2.html" >2</a> <a href="chap3.html" >3</a> <a href="chapBib.html" >Bib</a> </div >div class="chlinkprevnexttop" > <a href="chap0.html" >[Top of Book]</a> <a href="chap0.html#contents" >[Contents]</a> <a href="chap1.html" >[Next Chapter]</a> </div >"mathjaxlink" class="pcenter" ><a href="chap0_mj.html" >[MathJax on]</a></p>"X7D2C85EC87DD46E5" name="X7D2C85EC87DD46E5" ></a></p>div class="pcenter" >h1 >LieAlgDB</h1 >div >br />Email: <span class="URL" ><a href="mailto:cicalo@science.unitn.it" >cicalo@science.unitn.it</a></span >br />Address : <br />Dipartimento di Matematica e Informatica<br /> Via Ospedale 72<br /> Italy<br />br />Email: <span class="URL" ><a href="mailto:degraaf@science.unitn.it" >degraaf@science.unitn.it</a></span >br />Homepage: <span class="URL" ><a href="http://www.science.unitn.it/~degraaf " >http://www.science.unitn.it/~degraaf</a></span >br />Address : <br />Dipartimento di Matematica<br /> Via Sommarive 14<br /> Italy<br />br />Email: <span class="URL" ><a href="mailto:csaba@mat.ufmg.br" >csaba@mat.ufmg.br </a></span >br />Homepage: <span class="URL" ><a href="http://www.mat.ufmg.br/~csaba/ " >http://www.mat.ufmg.br /~csaba/</a></span >br />Address : <br />Departamento de Matemática<br /> Instituto de Ciências Exatas<br /> Universidade Federal de Minas Gerais (UFMG)<br /> Belo Horizonte, Brasil<br />"X7AA6C5737B711C89" name="X7AA6C5737B711C89" ></a></p>:</p>ul >li ><p>non-solvable Lie algebras over finite fields up to dimension 6;</p>li >li ><p>nilpotent Lie algebras of dimension up to 9 over <var class="Arg" >GF(2)</var >, of dimension up to 7 over <var class="Arg" >GF(3)</var > or <var class="Arg" >GF(5)</var >;</p>li >li ><p>simple Lie algebras of dimensions between 7 and 9 over <var class="Arg" >GF(2)</var >;</p>li >li ><p>the classification of solvable Lie algebras of dimension at most 4;</p>li >li ><p>the classification of nilpotent Lie algebras of dimensions at most 6.</p>li >ul >"X81488B807F2A1CF1" name="X81488B807F2A1CF1" ></a></p>strong class="pkg" >LieAlgDB</strong > package is free software; you can redistribute it and/or modify it under the terms of the <span class="URL" ><a href="http://www.fsf.org/licenses/gpl.html " >GNU General Public License</a></span > as published by the Free Software Foundation; either version 2 of the License, or (at your option ) any later version.</p>"X82A988D47DFAFCFA" name="X82A988D47DFAFCFA" ></a></p>ughan-Lee. Without their help, interest, and encouragement, this package would not have been made. We also acknowledge the effort of the referees to improve the implementation and the documentation.</p>ospitality during July - December 2009 and May - September 2010, when the classification of the 6-dimensional nilpotent Lie algebras over fields of characteristic 2 was made and added to the package.</p>"X8537FEB07AF2BEC8" name="X8537FEB07AF2BEC8" ></a></p>div class="contents" >"contents" name="contents" ></a></h3>div class="ContChap" ><a href="chap1.html#X7DFB63A97E67C0A1" >1 <span class="Heading" >Introduction</span ></a>div >div class="ContChap" ><a href="chap2.html#X7DD822827FAF0B46" >2 <span class="Heading" >The families of Lie algebras included in the database</span ></a>div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap2.html#X79B7688E808E0460" >2.1 <span class="Heading" >Non-solvable Lie algebras</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2.html#X8527F9157C850557" >2.1-1 NonSolvableLieAlgebra</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2.html#X82F0F10285A94949" >2.1-2 <span class="Heading" >Dimension 1 and 2</span ></a>span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2.html#X78C35F937D99AB14" >2.1-3 <span class="Heading" >Dimension 3</span ></a>span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2.html#X812516C97F0A1A4C" >2.1-4 <span class="Heading" >Dimension 4</span ></a>span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2.html#X865565C08312F7B0" >2.1-5 <span class="Heading" >Dimension 5</span ></a>span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2.html#X7FC5F0DB7A8CD1D0" >2.1-6 <span class="Heading" >Dimension 6</span ></a>span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2.html#X85CFDCF687153158" >2.1-7 AllNonSolvableLieAlgebras</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2.html#X7B54426D7B43CEF8" >2.1-8 AllSimpleLieAlgebras</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap2.html#X8697F2028731A29F" >2.2 <span class="Heading" >Solvable and nilpotent Lie algebras</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2.html#X81FDF3D17E495C6A" >2.2-1 SolvableLieAlgebra</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2.html#X7DA312A97A6242B4" >2.2-2 NilpotentLieAlgebra</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2.html#X8217183E7C19FA16" >2.2-3 AllSolvableLieAlgebras</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2.html#X86629DF87C2AEB4E" >2.2-4 AllNilpotentLieAlgebras</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2.html#X8770350D84304182" >2.2-5 NrNilpotentLieAlgebras</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2.html#X8068FF417F93FCD2" >2.2-6 LieAlgebraIdentification</a></span >div ></div >div >div class="ContChap" ><a href="chap3.html#X7BB72096877E0847" >3 <span class="Heading" >A description of the Lie algebras that are contained in the package</span ></a>div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap3.html#X7D10CF477EF901A7" >3.1 <span class="Heading" >Description of the non-solvable Lie algebras</span ></a>span >div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap3.html#X78C35F937D99AB14" >3.2 <span class="Heading" >Dimension 3</span ></a>span >div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap3.html#X812516C97F0A1A4C" >3.3 <span class="Heading" >Dimension 4</span ></a>span >div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap3.html#X865565C08312F7B0" >3.4 <span class="Heading" >Dimension 5</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3.html#X783B7FC180919CBC" >3.4-1 <span class="Heading" >Characteristic 2</span ></a>span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3.html#X80DAF658844AF393" >3.4-2 <span class="Heading" >Odd characteristic</span ></a>span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap3.html#X7FC5F0DB7A8CD1D0" >3.5 <span class="Heading" >Dimension 6</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3.html#X783B7FC180919CBC" >3.5-1 <span class="Heading" >Characteristic 2</span ></a>span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3.html#X7CC42FD178D384FD" >3.5-2 <span class="Heading" >General odd characteristic</span ></a>span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3.html#X7F4B0CC87A7715A5" >3.5-3 <span class="Heading" >Characteristic 3</span ></a>span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3.html#X81DD369B7F4E033B" >3.5-4 <span class="Heading" >Characteristic 5</span ></a>span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap3.html#X8411625F7E7DA71D" >3.6 <span class="Heading" >Description of the simple Lie algebras</span ></a>span >div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap3.html#X79FBD14A7959B5D2" >3.7 <span class="Heading" >Description of the solvable and nilpotent Lie algebras</span ></a>span >div >div >div class="ContChap" ><a href="chapBib.html" ><span class="Heading" >References</span ></a></div >br />div >div class="chlinkprevnextbot" > <a href="chap0.html" >[Top of Book]</a> <a href="chap0.html#contents" >[Contents]</a> <a href="chap1.html" >[Next Chapter]</a> </div >div class="chlinkbot" 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