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

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.

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Lie algebra cohomology, cohomology of equivariant sheaves
Mathematical Subject Classification 2010
Primary: 17B55
Secondary: 14L30
Received: 12 February 2020
Revised: 4 August 2020
Accepted: 10 October 2020
Published: 20 May 2021
Michael J. Larsen
Department of Mathematics
Indiana University
Bloomington, IN
United States
Valery A. Lunts
Department of Mathematics
Indiana University
Bloomington, IN
United States