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Jul 4, 2017 at 12:31 vote accept Ariel Weiss
Jul 4, 2017 at 11:29 comment added YCor "non-trivial" is not clearly defined: you probably mean non-abelian. Maybe you can tensor this rep to the standard rep of $SL_2$ and get something similar with non-abelian Lie algebra.
Jul 4, 2017 at 10:58 comment added Ariel Weiss Thanks for the answer! Do you know if there are any conditions that could be imposed to make this true? For example, in the case that I'm trying to apply this to, I have some information about the Lie algebra of $G$ -- in particular, I know that it's non-trivial.
Jul 3, 2017 at 19:56 history answered YCor CC BY-SA 3.0