Cohomology of Lie superalgebras $sl_{m|n}$ and $osp_{2|2n}$

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dc.creatorSu, Yucai
dc.creatorZhang, R. B.
dc.date2004-02-26
dc.date.accessioned2026-07-07T05:05:44Z
dc.date.available2026-07-07T05:05:44Z
dc.descriptionWe explicitly compute the first and second cohomology groups of the classical Lie superalgebras $sl_{m|n}$ and $osp_{2|2n}$ with coefficients in the finite dimensional irreducible modules and the Kac modules. We also show that the second cohomology groups of these Lie superalgebras with coefficients in the respective universal enveloping algebras (under the adjoint action) vanish. The latter result in particular implies that the universal enveloping algebras $U(sl_{m|n})$ and $U(osp_{2|2n})$ do not admit any non-trivial formal deformations of Gerstenhaber type.
dc.description42 pages
dc.identifierhttps://arxiv.org/abs/math/0402419
dc.identifierhttp://arxiv.org/abs/math/0402419
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/70279
dc.subjectQuantum Algebra
dc.subjectRepresentation Theory
dc.subject17B37; 20G42; 17B10
dc.titleCohomology of Lie superalgebras $sl_{m|n}$ and $osp_{2|2n}$
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