[GAP Forum] Lie Algebra Commutator Matrix Question

[Dima Pasechnik]

On Fri, May 14, 2021 at 11:17:53PM -0400, Alan Hylton wrote:
> I had a question about Lie algebras. Following some papers I've read, I'd
> like to see how I could calculate the rank of the commutator matrix. That
> is, if I build the multiplication table into a matrix, can GAP get its
> rank? I can do this in Maple, but it is very time consuming. I'd like to
> see how this works across platforms.

the multiplication table of an algebra is not really a numeric matrix,
it's a matrix of linear forms, with variables corresponding to generators.
(it's (i,j) entry is [g_i,g_j]=\sum_{k=1}^n c_{ij}^k g_k). So it's n x n x n tensor,
that you can variously slice into nxn matrices.

Could you be more specific in explaing  rank of what  you'd like to compute?

Dima