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Dec 13, 2021 at 11:08 comment added jvnv Thanks for your answer. I was aware of this proposition, and maybe I should have cited it from the beginning in the question (see update). However, the claim in [1] is about general connected Lie groups. The fact that the author uses structure theory to prove this for semi-simple Lie groups makes me wonder what an argument for the general case would be.
Dec 11, 2021 at 21:04 history edited LSpice CC BY-SA 4.0
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Dec 11, 2021 at 20:05 history answered Konstantinos Kanakoglou CC BY-SA 4.0