Detecting Cohomology for Lie Superalgebras

Details Detecting Cohomology for Lie Superalgebras Detecting Cohomology for Lie Superalgebras

2010-10-14

arxiv.org/abs/1010.3028v1

Mathematics

Representation Theory

Scientific paper

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 \cite{BKN1} and \cite{BaKN}, about realizing support varieties for Lie superalgebras via rank varieties constructed for the smaller detecting subalgebras.

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