############################################################################# ## #W README.wedderga The Wedderga package Osnel Broche Cristo #W Alexander Konovalov #W Aurora Olivieri #W Gabriela Olteanu #W Ãngel del RÃo ## #H $Id: README.wedderga,v 1.9 2008/01/28 14:39:10 alexk Exp $ ## ############################################################################# The 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. So the main functions of the package returns a list of simple algebras whose direct sum is isomorphic to the group algebra given as input. The methods implemented by the package produces the Wedderburn decomposition of a group algebra FG provided G is a finite group and F is either a finite field of characteristic coprime with the order of G, or an abelian number field (i.e. a subfield of a finite cyclotomic extension of the rationals). Other functions of Wedderga compute the primitive central idempotents of semisimple group algebras. The package also provides functions 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. Installation and system requirements: Wedderga does not use external binaries and, therefore, works without restrictions on the type of the operating system. It is designed for GAP4.4 and no compatibility with previous releases of GAP4 is guaranteed. To use the Wedderga online help it is necessary to install the GAP4 package GAPDoc by Frank Lübeck and Max Neunhöffer, which is available from the GAP site or from http://www.math.rwth-aachen.de/~Frank.Luebeck/GAPDoc/. Wedderga is distributed in standard formats (tar.gz, tar.bz2, -win.zip) and can be obtained from http://www.um.es/adelrio/wedderga.htm, its mirror http://www.cs.st-andrews.ac.uk/~alexk/wedderga.htm or the page http://www.gap-system.org/Packages/wedderga.html at the GAP web site. The latter also offers zoo-archive. To unpac the archive wedderga-4.3.2.zoo you need the program unzoo, which can be obtained from the GAP homepage http://www.gap-system.org (see section `Distribution'). To install Wedderga, copy this archive into the pkg subdirectory of your GAP 4.4 installation. The subdirectory wedderga will be created in the pkg directory after the following command: unzoo -x wedderga-4.3.2.zoo Installation *outside the GAP main directory*: when you don't have access to the directory of your main GAP installation you can also install the package by unpacking inside a directory "MYGAPDIR/pkg". Then to be able to load Wedderga you need to call GAP with the '-l ";MYGAPDIR" option. Installation using other archive formats is performed in a similar way. Now you can start GAP and load the Wedderga package using the command: gap> LoadPackage("wedderga"); Wedderga team January 2008