1. GAP
  2. Untitled project
  3. wedderga

Overview

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                           The Wedderga Package
                           --------------------
Osnel Broche Cristo, Allen Herman, Alexander Konovalov, Aurora Olivieri,
Gabriela Olteanu, Ángel del Río and Inneke Van Gelder.


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  and  a  complete  set  of  orthogonal  primitive 
idempotents.

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.

Furhermore, the package  provides functions to create code words from a group 
ring element.

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 GAP4.5 
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.cs.st-andrews.ac.uk/~alexk/wedderga/   or 
http://www.gap-system.org/Packages/wedderga.html  at  the  GAP web site.   To 
install Wedderga,  unpack its archive  into the pkg subdirectory  of your GAP
installation.  

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");



The Wedderga team                                               

November 2014