
arXiv: 1010.3028
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.
Mathematics(all), Lie bialgebras; Lie coalgebras, Group Theory (math.GR), Cohomology, Support varieties, Coadjoint orbits; nilpotent varieties, support varieties, detecting subalgebras, Detecting subalgebras, FOS: Mathematics, cohomology, Lie superalgebras, Representation Theory (math.RT), Mathematics - Group Theory, Mathematics - Representation Theory
Mathematics(all), Lie bialgebras; Lie coalgebras, Group Theory (math.GR), Cohomology, Support varieties, Coadjoint orbits; nilpotent varieties, support varieties, detecting subalgebras, Detecting subalgebras, FOS: Mathematics, cohomology, Lie superalgebras, Representation Theory (math.RT), Mathematics - Group Theory, Mathematics - Representation Theory
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