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Support varieties and
modules of finite projective dimension for modular Lie
superalgebras
Christopher M. Drupieski and Jonathan R. KujawaAppendix: Luchezar L. Avramov and Srikanth B. Iyengar |
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Vol. 15 (2021), No. 5, 1157–1180
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Abstract |
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We investigate cohomological support varieties for finite-dimensional Lie superalgebras defined over fields of odd characteristic. Verifying a conjecture from our previous work, we show the support variety of a finite-dimensional supermodule can be realized as an explicit subset of the odd nullcone of the underlying Lie superalgebra. We also show the support variety of a finite-dimensional supermodule is zero if and only if the supermodule is of finite projective dimension. As a consequence, we obtain a positive characteristic version of a theorem of Bøgvad, showing that if a finite-dimensional Lie superalgebra over a field of odd characteristic is absolutely torsion free, then its enveloping algebra is of finite global dimension. |
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Keywords
Lie superalgebras, cohomology, support varieties, rank
varieties, projective dimension
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Mathematical Subject Classification
Primary: 20G10
Secondary: 17B56
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Milestones
Received: 15 December 2019
Revised: 19 June 2020
Accepted: 21 November 2020
Published: 30 June 2021
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Authors |
| Christopher M. Drupieski | |
| Department of Mathematical
Sciences DePaul University Chicago, IL United States |
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| Jonathan R. Kujawa | |
| Department of Mathematics University of Oklahoma Norman, OK United States |
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| Luchezar L. Avramov | |
| Department of Mathematics University of Nebraska Lincoln, NE United States |
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| Srikanth B. Iyengar | |
| Department of Mathematics University of Utah Salt Lake City, Ut United States |
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