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I have a shallow understanding of group theory but until now it was sufficient. I'm trying to generalize a problem, it's a Lagrangian with SU(N) symmetry but I changed some basic quantity that makes calculations hard by using a general SU(N) representation basis. Hopefully the details of the problem are not important though, as I just want to rewrite these matrices in a more useful way. Say I have SU(4), it has 15 generators, right, so it looks plausible to replace this basis with 5 sets of SU(2) matrices instead. That would simplify my calculations! But looking at the actual matrices of SU(4) it's hard to see how to break them into SU(2) sets.

This seems to me like basic stuff I don't know. Anyone cares to nudge me in the right direction?