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Aug 31, 2015 at 16:19 vote accept Junekey Jeon
Aug 31, 2015 at 9:03 comment added S. Carnahan @JunekeyJeon Yes, if $G$ is connected, then $G$ is generated by exponentials of elements in the Lie algebra. This implies the two versions of invariance are the same.
Aug 30, 2015 at 2:26 comment added Junekey Jeon Wow, nice and simple counterexample! Thank you. So, what if G is connected? Is ad-invariance implies Ad-invariance for that case?
Aug 29, 2015 at 20:17 history answered S. Carnahan CC BY-SA 3.0