[GAP Forum] Decomposing rational modules

[degraaf at science.unitn.it]

Dear Dima, Peter, All,

In order to decompose a rational module, one can
compute its endomorphism algebra (i.e., all linear maps that
comute with the action of G). In this algebra one can find the
central idempotents. (That particular step is also implemented in GAP).
Those will give one the components that are direct sums of isotypical
modules. However, if the endomorphism algebra contains subalgebras
that are isomorphic to full matrix algebras, then one would have to
find complete sets of idempotents also in those algebras. That is an
extremely hard problem in general.

I hope the above makes sense.

All the best,

Willem