[GAP Forum] Extending fields of matrices.

[Derek Holt]

Dear James,

On Tue, Nov 18, 2008 at 01:26:05PM -0500, James B. Wilson wrote:
>
>
> V is a MeatAxe module over k=GF(p) and it is irreducible but
> not absolutely irreducible.
>
> How does one extend the field to the
> centralizing subfield of End V?
>
> I've found:
>
> MTX.IsAbsoluteIrreducible( V) and
> MTX.DegreeSplittingField( V)
>
> but how do I just reset the field?
>
> I would prefer to have, say, a matrix X in End V such
> that V is an absolutely irreducible k[X]-module, rather
> than an isomorphic copy of V over an isomorphic copy
> of k[X].  But if that is the only way it can be done, that is fine.

I think MTX.CentMat(V) returns the matrix X that you want.

Regards,
Derek Holt.