On associated variety for Lie superalgebras

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dc.creatorDuflo, M.
dc.creatorSerganova, V.
dc.date2005-07-11
dc.date.accessioned2026-07-07T05:21:34Z
dc.date.available2026-07-07T05:21:34Z
dc.descriptionWe define the associated variety $ X_{M} $ of a module $ M $ over a finite-dimensional superalgebra $ {\mathfrak g} $, and show how to extract information about $ M $ from these geometric data. $ X_{M} $ is a subvariety of the cone $ X $ of self-commuting odd elements. For finite-dimensional $ M $, $ X_{M} $ is invariant under the action of the underlying Lie group $ G_{0} $. For simple superalgebra with invariant symmetric form, $ X $ has finitely many $ G_{0} $-orbits; we associate a number (rank) to each such orbit. One can also associate a number (degree of atypicality) to an irreducible finite-dimensional representation. We prove that if $ M $ is an irreducible $ {\mathfrak g} $-module of degree of atypicality $ k $, then $ X_{M} $ lies in the closure of all orbits on $ X $ of rank $ k $. If $ {\mathfrak g}={\mathfrak g}{\mathfrak l}(m|n) $ we prove that $ X_{M} $ coincides with this closure.
dc.description21 pages
dc.identifierhttps://arxiv.org/abs/math/0507198
dc.identifierhttp://arxiv.org/abs/math/0507198
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/75737
dc.subjectRepresentation Theory
dc.subjectRings and Algebras
dc.titleOn associated variety for Lie superalgebras
dc.typetext

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