*[Corrected, thanks – T.]*

I was wondering why one need to take the ideal A to be of codimension 1? Already in the nilpotent case for example, i don’t see in which step we need A to satisfy that (also do we need H to be abelian?). I get the feeling that it is enough to be able to decompose the lie algebra into A \oplus H with A an ideal of the lie algebra.

Thanks for your answer!

Best regards

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