products/Sources/formale Sprachen/GAP/pkg/sla/doc/   (Algebra von RWTH Aachen Version 4.15.1©)  Datei vom 12.6.2024 mit Größe 14 kB image not shown  

Quelle  chap0.html   Sprache: HTML

 
 products/Sources/formale Sprachen/GAP/pkg/sla/doc/chap0.html


<?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 (SLA) - 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="chap4.html">4</a>  <a href="chap5.html">5</a>  <a href="chap6.html">6</a>  <a href="chapBib.html">Bib</a>  <a href="chapInd.html">Ind</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>

<p id="mathjaxlink" class="pcenter"><a href="chap0_mj.html">[MathJax on]</a></p>
<p><a id="X7D2C85EC87DD46E5" name="X7D2C85EC87DD46E5"></a></p>
<div class="pcenter">

<h1>SLA</h1>


<h2>Computing with simple Lie algebras</h2>

<p>
    Version 1.6.2</p>

<p>
    12 July 2024
  </p>

</div>
<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>
</p>

<p><a id="X7AA6C5737B711C89" name="X7AA6C5737B711C89"></a></p>
<h3>Abstract</h3>
<p>This package provides functions for computing with various aspects of the theory of simple Lie algebras in characteristic zero.</p>

<p><a id="X81488B807F2A1CF1" name="X81488B807F2A1CF1"></a></p>
<h3>Copyright</h3>
<p>© 2013-2018 Willem de Graaf</p>

<p><a id="X8537FEB07AF2BEC8" name="X8537FEB07AF2BEC8"></a></p>

<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#X84EA8FA47E4A7BDF">2 <span class="Heading">Root Systems and Weyl Groups</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap2.html#X7D22A7DF7EF96F24">2.1 <span class="Heading"> Root Systems </span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2.html#X8122C42F7CCFC6ED">2.1-1 ExtendedCartanMatrix</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2.html#X7DABAF857F49C8EB">2.1-2 CartanType</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2.html#X7BBD0ECE8762DB3A">2.1-3 DisplayDynkinDiagram</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap2.html#X808290B47CC22D62">2.2 <span class="Heading"> Weyl groups </span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2.html#X8789147A7A570A01">2.2-1 WeylTransversal</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2.html#X78A375CD80A0F31E">2.2-2 SizeOfWeylGroup</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2.html#X835F02DB7E5C1AF4">2.2-3 WeylGroupAsPermGroup</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2.html#X824D038880907771">2.2-4 ApplyWeylPermToWeight</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2.html#X79E8F3D5809EB6F8">2.2-5 WeylWordAsPerm</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2.html#X821242C278AA7C5F">2.2-6 PermAsWeylWord</a></span>
</div></div>
</div>
<div class="ContChap"><a href="chap3.html#X7944E8BD87DCAA24">3 <span class="Heading">Semisimple Lie Algebras and their Modules</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap3.html#X7844D90E7F25B423">3.1 <span class="Heading"> Semisimple Lie algebras </span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X7FA167DB80B7D701">3.1-1 IsomorphismOfSemisimpleLieAlgebras</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X7BBD0ECE8762DB3A">3.1-2 DisplayDynkinDiagram</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X7A83F8227DFEAAB2">3.1-3 ApplyWeylPermToCartanElement</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap3.html#X785D65257C93A7EF">3.2 <span class="Heading"> Representations of semisimple Lie algebras </span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X7866133B814EA2B2">3.2-1 AdmissibleLattice</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X7A4E769A87A9B2B3">3.2-2 DirectSumDecomposition</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X87A8E50683C5F286">3.2-3 IsIrreducibleHWModule</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X7EC5E998789DF177">3.2-4 HighestWeightVector</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X8488EF397B8298D6">3.2-5 HighestWeight</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X8589BB6484842CBC">3.2-6 DisplayHighestWeight</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X7B5CEF1E81AE0738">3.2-7 IsomorphismOfIrreducibleHWModules</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X79C8F1317C2E8C60">3.2-8 DualAlgebraModule</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X7889949D87615523">3.2-9 CharacteristicsOfStrata</a></span>
</div></div>
</div>
<div class="ContChap"><a href="chap4.html#X8295733081A2BFF8">4 <span class="Heading">Nilpotent Orbits</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap4.html#X8173135A7D187358">4.1 <span class="Heading"> The functions </span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X7A074A557A7347D2">4.1-1 NilpotentOrbit</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X7D5C0354810069A8">4.1-2 NilpotentOrbits</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X804830757E5971E9">4.1-3 WeightedDynkinDiagram</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X804830757E5971E9">4.1-4 WeightedDynkinDiagram</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X870F93A77E4F9CA7">4.1-5 DisplayWeightedDynkinDiagram</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X870F93A77E4F9CA7">4.1-6 DisplayWeightedDynkinDiagram</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X7F2B6308785707B9">4.1-7 AmbientLieAlgebra</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X8401CDC2859F8A85">4.1-8 SemiSimpleType</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X84E78DA17D8C7F74">4.1-9 SL2Triple</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X832FB68587166C4F">4.1-10 RandomSL2Triple</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X8029297A7C3372E9">4.1-11 SL2Grading</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X84E78DA17D8C7F74">4.1-12 SL2Triple</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X7E6926C6850E7C4E">4.1-13 Dimension</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X7CF02C4785F0EAB5">4.1-14 IsRegular</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X781CAF5D7FF46E66">4.1-15 RegularNilpotentOrbit</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X7A9088098391EB5E">4.1-16 IsDistinguished</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X80F0A7F07F78C06D">4.1-17 DistinguishedNilpotentOrbits</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X7CC92CF8796393CF">4.1-18 ComponentGroup</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X830C432A838875A0">4.1-19 InducedNilpotentOrbits</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X78795C607C2343C3">4.1-20 RigidNilpotentOrbits</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X856EEEB08169D020">4.1-21 RichardsonOrbits</a></span>
</div></div>
</div>
<div class="ContChap"><a href="chap5.html#X80D10A5D7D73D871">5 <span class="Heading">Finite Order Automorphisms and <span class="SimpleMath">θ</span>-Groups</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap5.html#X8173135A7D187358">5.1 <span class="Heading"> The functions </span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5.html#X856FF71D8565C1E5">5.1-1 FiniteOrderInnerAutomorphisms</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5.html#X7E8CCC4885E2A443">5.1-2 FiniteOrderOuterAutomorphisms</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5.html#X84F59A2687C62763">5.1-3 Order</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5.html#X8635ABCD7D5ACED8">5.1-4 KacDiagram</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5.html#X7DCA2568870A2D34">5.1-5 Grading</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5.html#X7D9BDD03811B3C98">5.1-6 NilpotentOrbitsOfThetaRepresentation</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5.html#X7D4106C37DBD0943">5.1-7 ClosureDiagram</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5.html#X8108B6487A3A363B">5.1-8 CarrierAlgebra</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5.html#X7A8D86667BC7C033">5.1-9 CartanSubspace</a></span>
</div></div>
</div>
<div class="ContChap"><a href="chap6.html#X7FF8A8057E0BFAFD">6 <span class="Heading">Semisimple Subalgebras of Semisimple Lie Algebras</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap6.html#X806713FE83F21540">6.1 <span class="Heading"> Branching </span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6.html#X8147807D7B92C613">6.1-1 ProjectionMatrix</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6.html#X806713FE83F21540">6.1-2 Branching</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap6.html#X7CC8010B7F31B486">6.2 <span class="Heading"> Constructing Semisimple Subalgebras </span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6.html#X7E95AD2C79B19D15">6.2-1 RegularSemisimpleSubalgebras</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6.html#X857808A77C13E46C">6.2-2 SSSTypes</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6.html#X832B17BA819FB057">6.2-3 LieAlgebraAndSubalgebras</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6.html#X82ECC8237E213AAB">6.2-4 InclusionsGraph</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6.html#X7C81C2B57D94EC2B">6.2-5 SubalgebrasInclusion</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6.html#X82458B807A8D77F6">6.2-6 DynkinIndex</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6.html#X7AAE2B317A4B7D9F">6.2-7 AreLinearlyEquivalentSubalgebras</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6.html#X7B1A01FE86A7718F">6.2-8 MakeDatabaseEntry</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6.html#X85A6B70B83A36495">6.2-9 ClosedSubsets</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6.html#X7A3EAA637F94D973">6.2-10 DecompositionOfClosedSet</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6.html#X798DF4D67DE56EB1">6.2-11 IsSpecialClosedSet</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6.html#X7D31AA9780B054C1">6.2-12 LieAlgebraOfClosedSet</a></span>
</div></div>
</div>
<div class="ContChap"><a href="chapBib.html"><span class="Heading">References</span></a></div>
<div class="ContChap"><a href="chapInd.html"><span class="Heading">Index</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"><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="chap4.html">4</a>  <a href="chap5.html">5</a>  <a href="chap6.html">6</a>  <a href="chapBib.html">Bib</a>  <a href="chapInd.html">Ind</a>  </div>

<hr />
<p class="foot">generated by <a href="https://www.math.rwth-aachen.de/~Frank.Luebeck/GAPDoc">GAPDoc2HTML</a></p>
</body>
</html>

99%


¤ Dauer der Verarbeitung: 0.2 Sekunden  (vorverarbeitet)  ¤

*© Formatika GbR, Deutschland




Wurzel

Suchen

Beweissystem der NASA

Beweissystem Isabelle

NIST Cobol Testsuite

Cephes Mathematical Library

Wiener Entwicklungsmethode

Haftungshinweis

Die Informationen auf dieser Webseite wurden nach bestem Wissen sorgfältig zusammengestellt. Es wird jedoch weder Vollständigkeit, noch Richtigkeit, noch Qualität der bereit gestellten Informationen zugesichert.

Bemerkung:

Die farbliche Syntaxdarstellung ist noch experimentell.