Abstract
Let \((\mathfrak{g}, [p]) \) 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 \(\operatorname{H}^\bullet(\mathfrak{u}(\mathfrak{g}), k)\) is finitely generated. This allows one to define support varieties for finite dimensional \(\mathfrak{u}(\mathfrak{g})\)-supermodules. We also show that support varieties for finite dimensional \(\mathfrak{u}(\mathfrak{g})\)- supermodules satisfy the desirable properties of a support variety theory.
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Presented by Jon F. Carlson
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Bagci, I. Cohomology and Support Varieties for Restricted Lie Superalgebras. Algebr Represent Theor 17, 213–225 (2014). https://doi.org/10.1007/s10468-012-9395-6
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DOI: https://doi.org/10.1007/s10468-012-9395-6