[GAP Forum] Query regarding the wedderga package

[Angel del Rio Mateos]

Dear Neha Makhijani,

The theory behind wedderga and details about implementation of wedderga 
is explained in the following papers:
I can provide copies of all of them if you are interested.
The thesis of Aurora Olivieri (in Spanish) and Gabriela Olteanu (in 
English) can be useful too.

1) Aurora Olivieri, Á. del Río y Juan Jacobo Simón
On monomial characters and central idempotents of rational group algebras
Communications in Algebra, 32 (2004), no. 4, 1531-1550

This was the first paper where we explained a character-free method to 
calculate Wedderburn decomposition and idempotents of rational group 
algebras which only applies for some finite groups that latter we 
decided to call strongly monomial. In this paper we prove that every 
abelian-by-supersolvable group is strongly monomial.

2) Aurora Olivieri y Á. del Río
An algorithm to compute the primitive central idempotents and the 
Wedderburn decomposition of a rational group algebra
Journal of Symbolic Computations, 35 (2003) 673-687

This paper explains the implementation of the first version of wedderga.
At this moment it only applies for rational group algebras of strongly 
monomial groups.

3) Osnel Broche Cristo y Á. del Río
Wedderburn decomposition of finite group algebras
Finite Fields and Their Applications 13 (2007) 71-79

In this paper we show how to extends the results of 1) to group algebras 
of strongly monomial groups with coefficients in finite fields. The 
second version of wedderga includes an implementation for this case.

4) G. Olteanu, Computing the Wedderburn decomposition of group algebras 
by the Brauer--Witt theorem, Math. Comp. 76 (2007), no. 258, 1073--1087.

This paper extended the method above to arbitrary groups.

5) Gabriela Olteanu y Á. del Río
An algorithm to compute the Wedderburn decomposition of semisimple group 
algebras implemented in the GAP package wedderga
Journal of Symbolic Computation 44 (2009) 507--516. 
doi:10.1016/j.jsc.2007.07.019

In this paper we explained the final implementation of wedderga which 
applies to semisimple group algebras over fields which are either finite 
or abelian extensions of the rationals.


-- 
Ángel del Río Mateos
Dep. Matemáticas, Univ. Murcia
30100 Murcia, Spain
Phone: +34 868 88 3537
Fax: +34 868 88 4182
http://www.um.es/adelrio/