A note on Lie algebra cohomology

Larsen, Michael J.; Lunts, Valery A.

doi:10.2140/ant.2021.15.773

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A note on Lie algebra cohomology

Michael J. Larsen and Valery A. Lunts

Vol. 15 (2021), No. 3, 773–783

DOI: 10.2140/ant.2021.15.773

Abstract

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

Keywords

Lie algebra cohomology, cohomology of equivariant sheaves

Mathematical Subject Classification 2010

Primary: 17B55

Secondary: 14L30

Milestones

Received: 12 February 2020

Revised: 4 August 2020

Accepted: 10 October 2020

Published: 20 May 2021

Authors

Michael J. Larsen
Department of Mathematics Indiana University Bloomington, IN United States

Valery A. Lunts
Department of Mathematics Indiana University Bloomington, IN United States

Vol. 15, No. 3, 2021