Lie superalgebra structures in cohomology spaces of Lie algebras with coefficients in the adjoint representation

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dc.creatorLebedev, Alexei
dc.creatorLeites, Dimitry
dc.creatorShereshevskii, Ilya
dc.date2004-04-06
dc.date.accessioned2026-07-07T06:20:01Z
dc.date.available2026-07-07T06:20:01Z
dc.descriptionThe space of Lie algebra cohomology is usually described by the dimensions of components of certain degree even for the adjoint module as coefficients when the spaces of cochains and cohomology can be endowed with a Lie superalgebra structure. Such a description is rather imprecise: these dimensions may coincide for cohomology spaces of distinct algebras. We explicitely describe the Lie superalgebras on the space of cohomology of the maximal nilpotent subalgebra of any simple finite dimensional Lie algebra. We briefly review related results by Grozman, Penkov and Serganova, Poletaeva, and Tolpygo. We cite a powerful Premet's theorem complementary to the Borel-Weil-Bott theorem. We mention relations with the Nijenhuis bracket and nonholonomic systems.
dc.identifierhttps://arxiv.org/abs/math/0404139
dc.identifierhttp://arxiv.org/abs/math/0404139
dc.identifierE.Vinberg (ed.) Lie groups and invariant theory, A.L.Onishchik Festschrift, Amer.Math.Soc.Transl.Ser.2, 213, Amer.Math.Soc., Providence, RI, 2005, 157-172
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/95224
dc.subjectK-Theory and Homology
dc.subjectDifferential Geometry
dc.subject17A70, 17B56 (Primary) 17B01, 17B70 (Secondary)
dc.titleLie superalgebra structures in cohomology spaces of Lie algebras with coefficients in the adjoint representation
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