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<h1>LieAlgDB</h1>


<h2>A database of Lie algebras</h2>

<p>
    2.3.0</p>

<p>
    24 September 2025
  </p>

</div>
<p><b>
    Serena Cicalò



  </b>
<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 />
</p><p><b>
    Willem Adriaan de Graaf




  </b>
<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 />
</p><p><b>
    Csaba Schneider




  </b>
<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 />
</p>

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<h3>Abstract</h3>
<p>This package provides access to the classification of the following families of Lie algebras:</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>
<p><a id="X81488B807F2A1CF1" name="X81488B807F2A1CF1"></a></p>
<h3>Copyright</h3>
<p>© 2006--2007 Willem de Graaf and Csaba Schneider</p>

<p>The <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>

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<h3>Acknowledgements</h3>
<p>We are grateful to Andrea Caranti, Marco Costantini, Bettina Eick, Helmut Strade, Michael Vaughan-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>

<p>Serena Cicalò would like to thank the Centro de Álgebra da Universidade de Lisboa for their kind hospitality 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>

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<div class="contents">
<h3>Contents<a id="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>
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<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2.html#X812516C97F0A1A4C">2.1-4 <span class="Heading">Dimension 4</span></a>
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<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>
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<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>
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<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap3.html#X78C35F937D99AB14">3.2 <span class="Heading">Dimension 3</span></a>
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<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>
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<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap3.html#X865565C08312F7B0">3.4 <span class="Heading">Dimension 5</span></a>
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<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>
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<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>
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<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>
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<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X7CC42FD178D384FD">3.5-2 <span class="Heading">General odd characteristic</span></a>
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<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X7F4B0CC87A7715A5">3.5-3 <span class="Heading">Characteristic 3</span></a>
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<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X81DD369B7F4E033B">3.5-4 <span class="Heading">Characteristic 5</span></a>
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<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>

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