Detecting cohomology for Lie superalgebras |
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Authors: | Gustav I. Lehrer Daniel K. Nakano Ruibin Zhang |
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Affiliation: | aSchool of Mathematics and Statistics, F07, University of Sydney, NSW 2006, Australia;bDepartment of Mathematics, University of Georgia, Athens, GA 30602, USA |
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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 Boe et al. (2010) [5] and Bagci et al. (2008) [2], about realizing support varieties for Lie superalgebras via rank varieties constructed for the smaller detecting subalgebras. |
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Keywords: | Lie superalgebras Cohomology Support varieties Detecting subalgebras |
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