Detecting Cohomology for Lie Superalgebras
Abstract
In this paper we use invariant theory to develop the notion of cohomological detection for Type I classical Lie superalgebras. In particular we show that the cohomology with coefficients in an arbitrary module can be detected on smaller subalgebras. These results are used later to affirmatively answer questions, which were originally posed in BKN1 and BaKN, about realizing support varieties for Lie superalgebras via rank varieties constructed for the smaller detecting subalgebras.
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