I'm writing some code that does simulations of quantum field theory, and I came to the sudden realization that I hadn't yet written the part for the SU(n) Lie group. I know this group is a subgroup of U(n) and GL(n), but GL is already infinite and U is also infinite as far as I know. Computers don't deal well with infinite sets, so I was wondering if there was a way I could compute the generators of the n-th SU group without having to examine all of GL
Cheers!
Well, after much research, I've figured it out. I have written a program that finds the roots of the special unitary group's Cartan matrix. I can use this information to find the generator matrices.
Special thanks to Batominovski, I got talking with Dr. Milev and we were able to solve the problem.
Cheers!