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Sleipnir
Sleipnir
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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 am looking for a proof in a textbook so that I can cite it. The result shows up in Weibel's book (Exercise 2.5.1), but only as an exercise (no proof) and only for rings. I could not find the result for Lie algebras.

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 am looking for a proof in a textbook so that I can cite it. The result shows up in Weibel's book (Exercise 2.5.1), but only as an exercise (no proof) and only for rings. I could not find the result for Lie algebras.

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 am looking for a proof in a textbook so that I can cite it. The result shows up in Weibel's book (Exercise 2.5.1), but only as an exercise (no proof).

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Sleipnir
Sleipnir
  • 95
  • 4

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 am looking for a proof in a textbook so that I can cite it. The result shows up in Weibel's book (Exercise 2.5.1), but only as an exercise (no proof) and only for rings. I could not find the result for Lie algebras.