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Representation Theory

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Cohomological finite generation for restricted Lie superalgebras and finite supergroup schemes

Author: Christopher M. Drupieski
Journal: Represent. Theory 17 (2013), 469-507
MSC (2010): Primary 17B56, 20G10; Secondary 17B55.
Published electronically: September 5, 2013
MathSciNet review: 3096330
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Abstract: We prove that the cohomology ring of a finite-dimensional restricted Lie superalgebra over a field of characteristic $p > 2$ is a finitely-generated algebra. Our proof makes essential use of the explicit projective resolution of the trivial module constructed by J. Peter May for any graded restricted Lie algebra. We then prove that the cohomological finite generation problem for finite supergroup schemes over fields of odd characteristic reduces to the existence of certain conjectured universal extension classes for the general linear supergroup $GL(m|n)$ that are similar to the universal extension classes for $GL_n$ exhibited by Friedlander and Suslin.

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Additional Information

Christopher M. Drupieski
Affiliation: Department of Mathematical Sciences, DePaul University, Chicago, Illinois 60614
MR Author ID: 924956
ORCID: 0000-0002-8250-1030

Received by editor(s): January 9, 2013
Received by editor(s) in revised form: May 8, 2013
Published electronically: September 5, 2013
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.