Support varieties for Lie superalgebras in characteristic 2

TL;DR

This paper explores cohomology and support varieties for Lie superalgebras over fields of characteristic 2, leveraging underlying Lie algebra structures to address open problems and establish unique results in this setting.

Contribution

It introduces new results on support varieties for Lie superalgebras in characteristic 2, utilizing the connection to ordinary Lie algebras to solve previously open issues.

Findings

Established existence of support varieties in characteristic 2

Linked superalgebra results to ordinary Lie algebra theory

Provided new insights specific to characteristic 2 case

Abstract

This paper investigates cohomology and support varieties for Lie superalgebras and restricted Lie superalgebras over a field of characteristic 2. The existence of an underlying ordinary Lie algebra allows us to obtain results that are still open in odd characteristic, and also to establish results that have no non-super analogues in characteristic 2.