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Nov 9, 2020 at 14:04 comment added Lezkus It is true that Q1 and Q2 are vague, in particular, Q1 could very well go as it is too vague. About Q2, I was not sure whether, for example, if $\mathfrak{g}$ is finite-dimensional real reductive then the simply connected $G$ given by Lie's third theorem is reductive, so that Q3 can be applied (this might very well be trivial, but I am not very used to work with reductive groups...). As I said, I think this belongs in mathstackexchange, but it got no love there so I reposted it here. In any case, thank you so much :)
Nov 9, 2020 at 13:31 comment added YCor Q1 and Q2 are quite vague and open-ended... Q2 sounds like "what are reductive subgroups of a reductive group?". For Q3 it seems to be a trivial yes (since $K$ is reductive)...
Nov 9, 2020 at 12:43 history asked Lezkus CC BY-SA 4.0