Cohomology and support varieties for Lie superalgebras

Details Cohomology and support varieties for Lie superalgebras Cohomology and support varieties for Lie superalgebras

2011-09-29

arxiv.org/abs/1109.6637v1

Mathematics

Representation Theory

Scientific paper

Let $mathfrak{g}$ be a restricted Lie superalgebra over an algebraically closed field $k$ of characteristic $p>2$. Let $\mathfrak{u}(\mathfrak{g})$ denote the restricted enveloping algebra of $\mathfrak{g}$. In this paper we prove that the cohomology ring $\HH^\bullet(\fu(\fg), k)$ is finitely generated. This allows one to define support varieties for finite dimensional $\fu(\fg)$-supermodules. We also show that support varieties for finite dimensional $\fu(\fg)$ supermodules satisfy the desirable properties of support variety theory.

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