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Jul 28 at 16:59 comment added Joshua Mundinger @LSpice good point, thank you. The second paragraph goes through perfectly well with $\mathcal Z^0$ everywhere instead of $\mathcal Z$.
Jul 28 at 16:47 comment added LSpice Although it's a nice touch, you don't need to handle disconnectedness of the centre; a compact Lie group is already the almost-direct product of the simply connected cover of its derived group and the maximal central torus--no need for the full centre, by your own second-paragraph argument about tangent spaces!
Jul 27 at 21:51 history answered Joshua Mundinger CC BY-SA 4.0