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Lie algebra cohomology with values in injective module

I am looking for a proof of the following result: Let $\mathfrak{g}$ be a Lie algebra and $I$ an injective $\mathfrak{g}$-module. Then $\mathrm{H}^q(\mathfrak{g},I)=0$ $\forall q>0$. More precisely, I …
3 votes
2 answers
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Universal central extension of Lie algebras

In the literature, there is the notion of the universal central extension of a Lie algebra. My question is: is there also a notion of universal extensions that are not central? If yes, can you provide …