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Dear GAP-Forum,

My question in short: do the generators in a MeatAxe-module have to be

_invertible_ matrices?

Explanation:

My question concerns MeatAxe, or more generally: modules for

associative algebras. I understand that MeatAxe is intended for

computations of modules over a group algebra (for example, in the

description of MeatAxe, it sais that the matrices that generate the

algebra must be invertible). However, from what I know about MeatAxe,

I think it should be usable for any associative algebra. Is that the

case?

Perhaps other methods have already been implemented for the application

I have in mind, which is the following. Given a Lie algebra G with a

subalgebra H, I want to test whether G/H is an irreducible H-module. One

can compute matrices for this action, simply by choosing a basis of G

of which a subset forms a basis of H, then computing the adjoint

matrices of the basis elements of H, and deleting rows and columns

that correspong to H. The resulting matrices are usually not

invertible. Is it still possible to use MeatAxe with them as input?

I tried a few small examples, which MeatAxe treated ok:

1. G=a simple lie algebra of type B2 with H=a maximal parabolic subalgebra

(of co-dimension 3, irreducible).

2. G=a simple lie algebra of type A2 with H=a maximal parabolic subalgebra

(of co-dimension 2, irreducible).

3. G=3*3-matrices with zeroes on positions (3,1) and (3,2), and

H=3*3-matrices with zero third row and zero third column.

(reducible).

Thanks in advance!

Jan Draisma

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