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<h1><strong class="pkg">Wedderga</strong></h1>


<h2>Wedderburn Decomposition of Group Algebras</h2>

<p>Version 4.11.1</p>

<p>07 July 2025</p>

</div>
<p><b>Gurmeet Kaur Bakshi 
          
          
  </b>
<br />Email: <span class="URL"><a href="mailto:gkbakshi@pu.ac.in">gkbakshi@pu.ac.in</a></span>
<br />Address: <br />Center for Advanced Study in Mathematics, <br /> Panjab University, Chandigarh, PIN-160014, India
</p><p><b>Osnel Broche Cristo 
          
          
  </b>
<br />Email: <span class="URL"><a href="mailto:osnel@ufla.br">osnel@ufla.br</a></span>
<br />Address: <br />Departamento de Ciências Exatas, Universidade Federal de Lavras - UFLA, Campus Universitário - Caixa Postal 3037, 37200-000, Lavras - MG, Brazil
</p><p><b>Allen Herman
          
       
           
  </b>
<br />Email: <span class="URL"><a href="mailto:aherman@math.uregina.ca">aherman@math.uregina.ca</a></span>
<br />Homepage: <span class="URL"><a href="http://www.math.uregina.ca/~aherman/">http://www.math.uregina.ca/~aherman/</a></span>
<br />Address: <br />Department of Mathematics and Statistics, <br /> University of Regina, <br /> 3737 Wascana Parkway, <br /> Regina, SK, S0G 0E0, Canada
</p><p><b>Olexandr Konovalov
          
       
           
  </b>
<br />Email: <span class="URL"><a href="mailto:obk1@st-andrews.ac.uk">obk1@st-andrews.ac.uk</a></span>
<br />Homepage: <span class="URL"><a href="https://alex-konovalov.github.io/">https://alex-konovalov.github.io/</a></span>
<br />Address: <br />School of Computer Science, University of St Andrews<br /> Jack Cole Building, North Haugh,<br /> St Andrews, Fife, KY16 9SX, Scotland
</p><p><b>Sugandha Maheshwary
          
           
  </b>
<br />Email: <span class="URL"><a href="mailto:msugandha@ma.iitr.ac.in">msugandha@ma.iitr.ac.in</a></span>
<br />Address: <br />Department of Mathematics<br /> Indian Institute of Technology Roorkee<br /> Roorkee, Uttarakhand 247667, India
</p><p><b>Aurora Olivieri
          
           
  </b>
<br />Email: <span class="URL"><a href="mailto:olivieri@usb.ve">olivieri@usb.ve</a></span>
<br />Address: <br />Departamento de Matemáticas<br /> Universidad Simón Bolívar<br /> Apartado Postal 89000, Caracas 1080-A, Venezuela
</p><p><b>Gabriela Olteanu
          
          
           
  </b>
<br />Email: <span class="URL"><a href="mailto:gabriela.olteanu@econ.ubbcluj.ro">gabriela.olteanu@econ.ubbcluj.ro</a></span>
<br />Homepage: <span class="URL"><a href="http://math.ubbcluj.ro/~olteanu">http://math.ubbcluj.ro/~olteanu</a></span>
<br />Address: <br />Department of Statistics-Forecasts-Mathematics<br /> Faculty of Economics and Business Administration<br /> Babes-Bolyai University<br /> Str. T. Mihali 58-60, 400591 Cluj-Napoca, Romania
</p><p><b>Ángel del Río
          
       
           
  </b>
<br />Email: <span class="URL"><a href="mailto:adelrio@um.es">adelrio@um.es</a></span>
<br />Homepage: <span class="URL"><a href="http://www.um.es/adelrio">http://www.um.es/adelrio</a></span>
<br />Address: <br />Departamento de Matemáticas, Universidad de Murcia<br /> 30100 Murcia, Spain
</p><p><b>Inneke Van Gelder
          
       
           
  </b>
<br />Email: <span class="URL"><a href="mailto:ivgelder@vub.ac.be">ivgelder@vub.ac.be</a></span>
<br />Homepage: <span class="URL"><a href="http://homepages.vub.ac.be/~ivgelder">http://homepages.vub.ac.be/~ivgelder</a></span>
<br />Address: <br />Vrije Universiteit Brussel, Departement Wiskunde <br /> Pleinlaan 2 <br /> 1050 Brussels, Belgium
</p>

<p><a id="X7AA6C5737B711C89" name="X7AA6C5737B711C89"></a></p>
<h3>Abstract</h3>
<p>``<strong class="pkg">Wedderga</strong>'' stands for ``<strong class="button">WEDDER</strong>burn decomposition of <strong class="button">G</strong>roup <strong class="button">A</strong>lgebras". This is a GAP package to compute the simple components of the Wedderburn decomposition of semisimple group algebras of finite groups over finite fields and over subfields of finite cyclotomic extensions of the rationals. It also contains functions that produce the primitive central idempotents of semisimple group algebras and a complete set of orthogonal primitive idempotents. Other functions of Wedderga allow to construct crossed products over a group with coefficients in an associative ring with identity and the multiplication determined by a given action and twisting.



<p><a id="X81488B807F2A1CF1" name="X81488B807F2A1CF1"></a></p>
<h3>Copyright</h3>
<p>© 2006-2025 by Gurmeet Kaur Bakshi, Osnel Broche Cristo, Allen Herman, Olexandr Konovalov, Sugandha Maheshwary, Aurora Olivieri, Gabriela Olteanu, Ángel del Río and Inneke Van Gelder.</p>

<p><strong class="pkg">Wedderga</strong> is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. For details, see the FSF's own site https://www.gnu.org/licenses/gpl.html.



<p>If you obtained <strong class="pkg">Wedderga</strong>, we would be grateful for a short notification sent to one of the authors. If you publish a result which was partially obtained with the usage of <strong class="pkg">Wedderga</strong>, please cite it in the following form:</p>

<p>G. K. Bakshi, O. Broche Cristo, A. Herman, O. Konovalov, S. Maheshwary, A. Olivieri, G. Olteanu, Á. del Río and I. Van Gelder. <em>Wedderga --- Wedderburn Decomposition of Group Algebras, Version 4.11.1;</em> 2025 (<span class="URL"><a href="https://gap-packages.github.io/wedderga/">https://gap-packages.github.io/wedderga/</a></span>).</p>

<p><a id="X82A988D47DFAFCFA" name="X82A988D47DFAFCFA"></a></p>
<h3>Acknowledgements</h3>
<p>We all are very grateful to Steve Linton for communicating the package and to the referee for careful testing <strong class="pkg">Wedderga</strong> and useful suggestions. Also we acknowledge very much the members of the <strong class="pkg">GAP</strong> team: Thomas Breuer, Alexander Hulpke, Frank Lübeck and many other colleagues for helpful comments and advise. We would like also to thank Thomas Breuer for the code of <code class="code">PrimitiveCentralIdempotentsByCharacterTable</code> for rational group algebras.</p>

<p>We gratefully acknowledge the support of Wedderga development by the following institutions:</p>


<ul>
<li><p>University of Murcia;</p>

</li>
<li><p>Francqui Stichting grant ADSI107;</p>

</li>
<li><p>M.E.C. of Romania (CEEX-ET 47/2006);</p>

</li>
<li><p>D.G.I. of Spain;</p>

</li>
<li><p>Fundación Séneca of Murcia;</p>

</li>
<li><p>CAPES and FAPESP of Brazil;</p>

</li>
<li><p>Research Foundation Flanders (FWO - Vlaanderen);</p>

</li>
<li><p>CCP CoDiMa (EP/M022641/1);</p>

</li>
<li><p>Department of Science and Technology (DST), India.</p>

</li>
</ul>
<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 class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap1.html#X7F8C3A087C875426">1.1 <span class="Heading">General aims of <strong class="pkg">Wedderga</strong> package</span></a>
</span>
</div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap1.html#X7DB566D5785B7DBC">1.2 <span class="Heading">Installation and system requirements</span></a>
</span>
</div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap1.html#X7EC3E10184435AC0">1.3 <span class="Heading">Main functions of <strong class="pkg">Wedderga</strong> package</span></a>
</span>
</div>
</div>
<div class="ContChap"><a href="chap2.html#X87273420791F220E">2 <span class="Heading">Wedderburn decomposition</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap2.html#X7C902C667D137851">2.1 <span class="Heading">Wedderburn decomposition of a group algebra</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2.html#X7F1779ED8777F3E7">2.1-1 WedderburnDecomposition</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2.html#X8710F98A85F0DD29">2.1-2 WedderburnDecompositionInfo</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap2.html#X7D06959F7D444C55">2.2 <span class="Heading">Simple quotients</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2.html#X8349114C83161C2D">2.2-1 SimpleAlgebraByCharacter</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2.html#X876FD2367E64462D">2.2-2 SimpleAlgebraByCharacterInfo</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2.html#X812D667D7D913EB5">2.2-3 SimpleAlgebraByStrongSP</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2.html#X858152C882129A0B">2.2-4 SimpleAlgebraByStrongSPInfo</a></span>
</div></div>
</div>
<div class="ContChap"><a href="chap3.html#X80C058BE81824B23">3 <span class="Heading">Shoda pairs</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap3.html#X8072BA2B87199557">3.1 <span class="Heading">Computing extremely strong Shoda pairs</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X86B2AFF87D26FC75">3.1-1 ExtremelyStrongShodaPairs</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap3.html#X807C74B07C4B99AF">3.2 <span class="Heading">Computing strong Shoda pairs</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X820A398687A79B9D">3.2-1 StrongShodaPairs</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap3.html#X7B49C1BC834E57E3">3.3 <span class="Heading">Properties related with Shoda pairs</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X7A851A00809B4C92">3.3-1 IsExtremelyStrongShodaPair</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X7C17476F854F1E34">3.3-2 IsStrongShodaPair</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X823B8DEC7ECC3326">3.3-3 IsShodaPair</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X80C4ED17809FC547">3.3-4 IsStronglyMonomial</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X8485C39787CF0797">3.3-5 IsNormallyMonomial</a></span>
</div></div>
</div>
<div class="ContChap"><a href="chap4.html#X7C651C9C78398FFF">4 <span class="Heading">Idempotents</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap4.html#X7DF49142844C278D">4.1 <span class="Heading">Computing idempotents from character table</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X7BBEB4A084DBF0D6">4.1-1 PrimitiveCentralIdempotentsByCharacterTable</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap4.html#X83F7CF1E87D02581">4.2 <span class="Heading">Testing lists of idempotents for completeness</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X81FCD27E812078F0">4.2-1 IsCompleteSetOfOrthogonalIdempotents</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap4.html#X7C66102485AF5F80">4.3 <span class="Heading">Idempotents from Shoda pairs</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X78D597207D3030EA">4.3-1 PrimitiveCentralIdempotentsByESSP</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X7B48EE1A7ECAB151">4.3-2 PrimitiveCentralIdempotentsByStrongSP</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X82460B1285A0A7D7">4.3-3 PrimitiveCentralIdempotentsBySP</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap4.html#X8577F9547FC58C4C">4.4 <span class="Heading">Complete set of orthogonal primitive idempotents from Shoda pairs and cyclotomic classes</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X7E95CDF17C4D54DB">4.4-1 PrimitiveIdempotentsNilpotent</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X8784570980B9B750">4.4-2 PrimitiveIdempotentsTrivialTwisting</a></span>
</div></div>
</div>
<div class="ContChap"><a href="chap5.html#X812A5A097EADEB5E">5 <span class="Heading">Crossed products and their elements</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap5.html#X79122C7F877430A7">5.1 <span class="Heading">Construction of crossed products</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5.html#X797F31EF7B51A4DF">5.1-1 CrossedProduct</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap5.html#X8560A2F37B608A9F">5.2 <span class="Heading">Crossed product elements and their properties</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5.html#X7D2313AA82F1D5CC">5.2-1 ElementOfCrossedProduct</a></span>
</div></div>
</div>
<div class="ContChap"><a href="chap6.html#X7D3C0B1F7A66056F">6 <span class="Heading">Useful properties and functions</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap6.html#X7BA5D68A86B8C772">6.1 <span class="Heading">Semisimple group algebras of finite groups</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6.html#X7EF856E880722311">6.1-1 IsSemisimpleZeroCharacteristicGroupAlgebra</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6.html#X85999B6A7C52E305">6.1-2 IsSemisimpleRationalGroupAlgebra</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6.html#X79289F7F7FC04846">6.1-3 IsSemisimpleANFGroupAlgebra</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6.html#X7B546E2D7FB561BA">6.1-4 IsSemisimpleFiniteGroupAlgebra</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6.html#X8337F25387C53B02">6.1-5 IsTwistingTrivial</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap6.html#X86121BD77F7E5C7A">6.2 <span class="Heading">Operations with group rings elements</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6.html#X7A2BF4527E08803C">6.2-1 Centralizer</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6.html#X7FE417DD837987B4">6.2-2 OnPoints</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6.html#X798CEA1F80D355EE">6.2-3 AverageSum</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap6.html#X7AAB3882785C04E0">6.3 <span class="Heading">Cyclotomic classes</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6.html#X7D7BDF5087C8F4C6">6.3-1 CyclotomicClasses</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6.html#X7FA101AE7BC33671">6.3-2 IsCyclotomicClass</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap6.html#X7B16423A7FBED034">6.4 <span class="Heading">Other commands</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6.html#X872510997A7AF31D">6.4-1 InfoWedderga</a></span>
</div></div>
</div>
<div class="ContChap"><a href="chap7.html#X7B5D5E628144C0A2">7 <span class="Heading">Functions for calculating Schur indices and identifying division algebras</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap7.html#X7802E175859EEB53">7.1 <span class="Heading">Main Schur Index and Division Algebra Functions</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X854DF62880C118B8">7.1-1 WedderburnDecompositionWithDivAlgParts</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X83BC82867BE66A0B">7.1-2 CyclotomicAlgebraWithDivAlgPart</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X7D065D65858428A6">7.1-3 SchurIndex</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X860975A4792E119D">7.1-4 WedderburnDecompositionAsSCAlgebras</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap7.html#X81198A8B7C19978A">7.2 <span class="Heading">Cyclotomic Reciprocity Functions </span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X78482C2B7959526E">7.2-1 PPartOfN</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X7F4F73E887C96737">7.2-2 PSplitSubextension</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X7845830082B7C723">7.2-3 SplittingDegreeAtP</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap7.html#X84506474869914E0">7.3 <span class="Heading">Global Splitting and Character Descent Functions </span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X80B04A237F4C19FF">7.3-1 GlobalSplittingOfCyclotomicAlgebra</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X81FBABAB856C676F">7.3-2 CharacterDescent</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X8106A02C78BFD852">7.3-3 GaloisRepsOfCharacters</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X782BE5F8844158AD">7.3-4 WedderburnDecompositionByCharacterDescent</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap7.html#X8405EF4D8264030A">7.4 <span class="Heading">Local index functions for Cyclic Cyclotomic Algebras</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X8780F8E87B6EC023">7.4-1 LocalIndicesOfCyclicCyclotomicAlgebra</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X78588B587AEDD22F">7.4-2 LocalIndexAtInfty</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap7.html#X85FBEBDA787CD61E">7.5 <span class="Heading">Local index functions for Non-Cyclic Cyclotomic Algebras</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X798DCABC8228F2DE">7.5-1 LocalIndicesOfCyclotomicAlgebra</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X86AE281C7C69E42C">7.5-2 RootOfDimensionOfCyclotomicAlgebra</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X7F33FE4F7E029BF7">7.5-3 DefiningGroupOfCyclotomicAlgebra</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X8656B34387EC74EF">7.5-4 LocalIndexAtInftyByCharacter</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X7A3FB2D9846974CD">7.5-5 DefectGroupOfConjugacyClassAtP</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X80D1046284577B32">7.5-6 LocalIndexAtPByBrauerCharacter</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X82A979548619CB85">7.5-7 LocalIndexAtOddPByCharacter</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap7.html#X82E9840B843D666E">7.6 <span class="Heading">Local index functions for Rational Quaternion Algebras</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X78E6B3807EDDE82E">7.6-1 LocalIndicesOfRationalQuaternionAlgebra</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X79071DD8853678C0">7.6-2 IsRationalQuaternionAlgebraADivisionRing</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap7.html#X8164EAE07A90DB11">7.7 <span class="Heading">Functions involving Cyclic Algebras</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X8671E3BD788B709F">7.7-1 DecomposeCyclotomicAlgebra</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X8129F9307969D473">7.7-2 ConvertCyclicAlgToCyclicCyclotomicAlg</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X81FAC27A829D5FF9">7.7-3 ConvertQuaternionAlgToQuadraticAlg</a></span>
</div></div>
</div>
<div class="ContChap"><a href="chap8.html#X83FD4D318127261B">8 <span class="Heading">Applications of the Wedderga package</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap8.html#X8582FB957C58DFB3">8.1 <span class="Heading">Coding theory applications</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap8.html#X7AE55D3C7BFCF3A9">8.1-1 CodeWordByGroupRingElement</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap8.html#X7C8BBBDB78A1678E">8.1-2 CodeByLeftIdeal</a></span>
</div></div>
</div>
<div class="ContChap"><a href="chap9.html#X840E625A81FDAEC6">9 <span class="Heading">The basic theory behind <strong class="pkg">Wedderga</strong></span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap9.html#X815ECCD97B18314B">9.1 <span class="Heading">Group rings and group algebras</span></a>
</span>
</div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap9.html#X7FDD93FB79ADCC91">9.2 <span class="Heading">Semisimple group algebras</span></a>
</span>
</div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap9.html#X84BB4A6081EAE905">9.3 <span class="Heading">Wedderburn components</span></a>
</span>
</div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap9.html#X87B6505C7C2EE054">9.4 <span class="Heading">Characters and primitive central idempotents</span></a>
</span>
</div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap9.html#X7A24D5407F72C633">9.5 <span class="Heading">Central simple algebras and Brauer equivalence</span></a>
</span>
</div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap9.html#X7FB21779832CE1CB">9.6 <span class="Heading">Crossed Products</span></a>
</span>
</div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap9.html#X828C42CD86AF605F">9.7 <span class="Heading">Cyclic Crossed Products</span></a>
</span>
</div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap9.html#X7869E2A48784C232">9.8 <span class="Heading">Abelian Crossed Products</span></a>
</span>
</div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap9.html#X80BABE5078A29793">9.9 <span class="Heading">Classical crossed products</span></a>
</span>
</div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap9.html#X84C98BB8859BBEE2">9.10 <span class="Heading">Cyclic Algebras</span></a>
</span>
</div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap9.html#X8099A8C784255672">9.11 <span class="Heading">Cyclotomic algebras</span></a>
</span>
</div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap9.html#X84A142407B7565E0">9.12 <span class="Heading">Numerical description of cyclotomic algebras</span></a>
</span>
</div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap9.html#X8310E96086509397">9.13 <span class="Heading">Idempotents given by subgroups</span></a>
</span>
</div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap9.html#X7D518BAB80EDE190">9.14 <span class="Heading">Shoda pairs of a group</span></a>
</span>
</div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap9.html#X7E3479527BAE5B9E">9.15 <span class="Heading">Strong Shoda pairs of a group</span></a>
</span>
</div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap9.html#X81B5CE0378DC4913">9.16 <span class="Heading">Extremely strong Shoda pairs of a group</span></a>
</span>
</div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap9.html#X84C694978557EFE5">9.17 <span class="Heading">Strongly monomial characters and strongly monomial groups</span></a>
</span>
</div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap9.html#X7C8D47C180E0ACAD">9.18 <span class="Heading">Normally monomial characters and normally monomial groups</span></a>
</span>
</div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap9.html#X800D8C5087D79DC8">9.19 <span class="Heading">Cyclotomic Classes and Strong Shoda Pairs</span></a>
</span>
</div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap9.html#X803562E087325AF6">9.20 <span class="Heading">Theory for Local Schur Index and Division Algebra Part Calculations</span></a>
</span>
</div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap9.html#X7B18AF347AE68020">9.21 <span class="Heading"> Obtaining Algebras with structure constants as terms of the Wedderburn decomposition </span></a>
</span>
</div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap9.html#X8472ACCF802EC188">9.22 <span class="Heading">A complete set of orthogonal primitive idempotents</span></a>
</span>
</div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap9.html#X856D7975810BF987">9.23 <span class="Heading">Applications to coding theory</span></a>
</span>
</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>
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