How would one prove that a maximal torus in a lie group is a maximal abelian subgroup? For example, in the specific cases of SO(n) or SU(n). I know that the maximal torus of SO(2n) and SO(2n+1) is Tn and that of SU(n) is Tn-1, and by definition, the maximal torus is an abelian subgroup, but I'm having trouble showing that it is maximal.
2026-05-06 08:55:24.1778057724
Maximal tori in lie groups?
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