## &Wedderga;

Wedderburn Decomposition of Group Algebras
Version 4.2
Osnel Broche Cristo osnelier@ime.usp.br

              Departamento de Matemática

              Instituto de Ciências Exatas

              Universidade Federal de Juiz de Fora

              Campus-Cidade Universitária, 36036-900, Juiz de Fora

Alexander Konovalov konovalov@member.ams.org http://www.cs.st-andrews.ac.uk/˜alexk/

              School of Computer Science, University of St Andrews

              Jack Cole Building, North Haugh,

              St Andrews, Fife, KY16 9SX, Scotland

Aurora Olivieri olivieri@usb.ve

              Departamento de Matemáticas

    	      Universidad Simón Bolívar

              Apartado Postal 89000, Caracas 1080-A, Venezuela

Gabriela Olteanu golteanu@um.es, olteanu@math.ubbcluj.ro

              Departamento de Matemáticas, Universidad de Murcia

              30100 Murcia, Spain

Ángel del Río adelrio@um.es http://www.um.es/adelrio

              Departamento de Matemáticas, Universidad de Murcia

              30100 Murcia, Spain

March 2007

&Wedderga; package The title ``&Wedderga;'' stands for ``WEDDERburn decomposition of Group Algebras. 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 rational. It also contains functions that produce the primitive central idempotents of semisimple group algebras. Other functions of &Wedderga; allows 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.

&copyright; 2006-2007 by Osnel Broche Cristo, Alexander Konovalov, Aurora Olivieri, Gabriela Olteanu and Ángel del Río.

&Wedderga; 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 http://www.gnu.org/licenses/gpl.html.

If you obtained &Wedderga;, 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 &Wedderga;, please cite it in the following form:

O. Broche Cristo, A. Konovalov, A. Olivieri, G. Olteanu and Á. del Río. Wedderga --- Wedderburn Decomposition of Group Algebras, Version 4.2; 2007 (http://www.um.es/adelrio/wedderga.htm).
We all are very grateful to Steve Linton for communicating the package and to the referee for careful testing &Wedderga; and useful suggestions. Also we acknowledge very much the members of the &GAP; 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 PrimitiveCentralIdempotentsByCharacterTable for rational group algebras.

On various stages the development of the Wedderga package was supported by the following institutions: University of Murcia; Francqui Stichting grant ADSI107; M.E.C. of Romania (CEEX-ET 47/2006); D.G.I. of Spain; Fundación Séneca of Murcia. We acknowledge with gratitude this support.

<#Include SYSTEM "intro.xml"> <#Include SYSTEM "decomp.xml"> <#Include SYSTEM "SSP.xml"> <#Include SYSTEM "idempot.xml"> <#Include SYSTEM "crossed.xml"> <#Include SYSTEM "auxiliar.xml"> <#Include SYSTEM "theory.xml">