#### Vol. 15, No. 3, 2021

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A note on Lie algebra cohomology

### Michael J. Larsen and Valery A. Lunts

Vol. 15 (2021), No. 3, 773–783
##### Abstract

Given a finite dimensional Lie algebra $L$, let $I$ be the augmentation ideal in the universal enveloping algebra $U\phantom{\rule{-0.17em}{0ex}}\left(L\right)$. We study the conditions on $L$ under which the $Ext$-groups $Ext\left(k,k\right)$ for the trivial $L$-module $k$ are the same when computed in the category of all $U\phantom{\rule{-0.17em}{0ex}}\left(L\right)$-modules or in the category of $I$-torsion $U\phantom{\rule{-0.17em}{0ex}}\left(L\right)$-modules. An application to cohomology of equivariant sheaves is given.

##### Keywords
Lie algebra cohomology, cohomology of equivariant sheaves
Primary: 17B55
Secondary: 14L30