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Detecting cohomology for Lie superalgebras

Authors: Lehrer, Gustav I.; Nakano, Daniel K.; Zhang, Ruibin;

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

Keywords

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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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
8
Average
Top 10%
Average
Green
hybrid