## Cohomological finite generation for restricted Lie superalgebras and finite supergroup schemes

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- by Christopher M. Drupieski
- Represent. Theory
**17**(2013), 469-507 - DOI: https://doi.org/10.1090/S1088-4165-2013-00440-5
- Published electronically: September 5, 2013
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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.## References

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## Bibliographic Information

**Christopher M. Drupieski**- Affiliation: Department of Mathematical Sciences, DePaul University, Chicago, Illinois 60614
- MR Author ID: 924956
- ORCID: 0000-0002-8250-1030
- Email: cdrupies@depaul.edu
- Received by editor(s): January 9, 2013
- Received by editor(s) in revised form: May 8, 2013
- Published electronically: September 5, 2013
- © Copyright 2013
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication. - Journal: Represent. Theory
**17**(2013), 469-507 - MSC (2010): Primary 17B56, 20G10; Secondary 17B55
- DOI: https://doi.org/10.1090/S1088-4165-2013-00440-5
- MathSciNet review: 3096330