On the finite generation of relative cohomology for Lie superalgebras

Maurer, Andrew

doi:10.1090/proc/14345

On the finite generation of relative cohomology for Lie superalgebras
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Proc. Amer. Math. Soc. 147 (2019), 1897-1910 Request permission

Abstract:

The author establishes the finite generation of the cohomology ring of a classical Lie superalgebra relative to an even subsuperalgebra. A spectral sequence is constructed to provide conditions for when this relative cohomology ring is Cohen–Macaulay. With finite generation established, support varieties for modules are defined via the relative cohomology, which generalize those of Boe, Kujawa, and Nakano [Trans. Amer. Math. Soc. 262 (2010), no. 12, 6551-6590].

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