[GAP Forum] Convolutive algebra over a finite group

[Thomas Breuer]

Dear GAP Forum,

Stefano Simonucci asked

> I have known that the irreducible representations of a finite group is 
> related to the ideals of a convolutive algebra over the group. 
> I don't know if it is possible to build this algebra, starting from the 
> structure of the group, by means of GAP.

I am not sure whether Stefano means the group algebra,
but this is closely related to the representations
of a group is the group algebra.

The GAP library contains basic support for creating group algebras,
see section ``GroupRing'' in the GAP Reference Manual,
for example `http://www.gap-system.org/Manuals/doc/htm/ref/CHAP063.htm'.
Special functions for group rings can be found in the GAP package ``laguna'',
see `http://www.gap-system.org/Packages/laguna.html'.

For questions concerning the centre of a group algebra,
also the character theory stuff in GAP may be of interest,
see chapter ``Character Tables'' in the GAP Reference Manual,
for example `http://www.gap-system.org/Manuals/doc/htm/ref/CHAP069.htm'.

All the best,
Thomas Breuer