Wedderburn Decomposition of Group Algebras

Version 4.10.0

Released 2020-05-15

This project is maintained by Gurmeet Kaur Bakshi, Osnel Broche Cristo, Allen Herman, Alexander Konovalov, Sugandha Maheshwary, Gabriela Olteanu, Aurora Olivieri, Angel del Rio, 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, and calculate Schur indices of simple 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.

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

Wedderga does not use external binaries and, therefore, works without restrictions on the type of the operating system. It is redistributed with GAP, but is not loaded by default. Therefore, to use Wedderga, first you need to load it using the following command:

```
gap> LoadPackage("wedderga");
```

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