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# Wedderga

## Wedderburn Decomposition of Group Algebras

Version 4.9.1

11 December 2017

Gurmeet Kaur Bakshi
Email: gkbakshi@pu.ac.in
Center for Advanced Study in Mathematics,
Panjab University, Chandigarh, PIN-160014, India

Osnel Broche Cristo
Email: osnel@ufla.br
Departamento de Ciências Exatas, Universidade Federal de Lavras - UFLA, Campus Universitário - Caixa Postal 3037, 37200-000, Lavras - MG, Brazil

Allen Herman
Email: aherman@math.uregina.ca
Homepage: http://www.math.uregina.ca/~aherman/
Department of Mathematics and Statistics,
University of Regina,
3737 Wascana Parkway,

Alexander Konovalov
Email: alexk@mcs.st-andrews.ac.uk
Homepage: 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

Sugandha Maheshwary
Email: sugandha@iisermohali.ac.in
Department of Mathematical Sciences
Indian Institute of Science Education and Research
Mohali, Knowledge city, Sector 81, SAS Nagar,
Manauli, PO 140306, India

Aurora Olivieri
Email: olivieri@usb.ve
Departamento de Matemáticas
Apartado Postal 89000, Caracas 1080-A, Venezuela

Gabriela Olteanu
Email: gabriela.olteanu@econ.ubbcluj.ro
Homepage: http://math.ubbcluj.ro/~olteanu
Department of Statistics-Forecasts-Mathematics
Babes-Bolyai University
Str. T. Mihali 58-60, 400591 Cluj-Napoca, Romania

Ángel del Río
Departamento de Matemáticas, Universidad de Murcia
30100 Murcia, Spain

Inneke Van Gelder
Email: ivgelder@vub.ac.be
Homepage: http://homepages.vub.ac.be/~ivgelder
Vrije Universiteit Brussel, Departement Wiskunde
Pleinlaan 2
1050 Brussels, Belgium

### Abstract

Wedderga'' stands for burn decomposition of roup 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.

© 2006-2017 by Gurmeet Kaur Bakshi, Osnel Broche Cristo, Allen Herman, Alexander Konovalov, Sugandha Maheshwary, Aurora Olivieri, Gabriela Olteanu, Ángel del Río and Inneke Van Gelder.

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:

G. K. Bakshi, O. Broche Cristo, A. Herman, A. Konovalov, S. Maheshwary, A. Olivieri, G. Olteanu, Á. del Río and I. Van Gelder. Wedderga --- Wedderburn Decomposition of Group Algebras, Version 4.9.1; 2017 (http://www.cs.st-andrews.ac.uk/~alexk/wedderga).

### Acknowledgements

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.

We gratefully acknowledge the support of Wedderga development by the following institutions:

• University of Murcia;

• M.E.C. of Romania (CEEX-ET 47/2006);

• D.G.I. of Spain;

• Fundación Séneca of Murcia;

• CAPES and FAPESP of Brazil;

• Research Foundation Flanders (FWO - Vlaanderen);

• CCP CoDiMa (EP/M022641/1);

• Department of Science and Technology (DST), India.

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