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. Thanks! On Sat, May 15, 2021 at 9:01 AM Dima Pasechnik <[email protected]> wrote: > 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 > _______________________________________________ Forum mailing list [email protected] https://mail.gap-system.org/mailman/listinfo/forum
