[GAP Forum] Lie Algebra Commutator Matrix Question

[Bill Allombert]

On Sun, May 16, 2021 at 01:33:46AM -0400, Alan Hylton wrote:
> Hi Dima,
> 
> And thanks for the reply!
> 
> Yes, this is a bit weird - I admit it. Following some research I've seen
> into certain index computations, I need to essentially create my
> multiplication table, and essentially view the vectors as indeterminates.
> So if I had a Lie algebra spanned by e1 and e2, and [e1, e2] = 2e2, then
> the multiplication table would be a 2x2 matrix with E_12 = 2e2 and 0's
> elsewhere. If I view e2 as an indeterminate, then, this matrix has rank 1.

So to be sure, you want the rank over the rational function field C(e1,e2),
and your issue when using Maple on larger example is that such linear
algebra computation is too slow, or is it computing the matrix ?

Cheers,
Bill.