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Dec 12, 2013 at 23:09 comment added LSpice To me, it is marvellous that the failure of this fact (as opposed to the truth of the corresponding fact for $\operatorname{SL}(2, \mathbb C)$) is a matter of topology; that is, from the point of view of algebraic groups, it comes from the fact that $\operatorname{SL}(2, \mathbb C)$ is simply connected, whereas $\operatorname{PSL}(2, \mathbb C)$ (which I had rather call $\operatorname{PGL}(2, \mathbb C)$) is not (it is at the opposite extreme---`adjoint').
May 11, 2011 at 13:00 history answered Ben McKay CC BY-SA 3.0