Indecomposable representations of Lie superalgebras

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dc.creatorLeites, Dimitry
dc.date2002-02-18
dc.date.accessioned2026-07-07T04:46:33Z
dc.date.available2026-07-07T04:46:33Z
dc.descriptionIn 1960's I. Gelfand posed a problem: describe indecomposable representations of any simple infinite dimensional Lie algebra of polynomial vector fields. Here, by applying the elementary technique of Gelfand and Ponomarev, a toy model of the problem is solved: finite dimensional indecomposable representations of vect(0|2), the Lie superalgebra of vector fields on the (0|2)-dimensional superspace, are described. Since vect (0|2) is isomorphic to sl(1|2) and osp(2|2), their representations are also described. The result is generalized in two directions: for sl(1|n) and osp(2|2n). Independently and differently J. Germoni described indecomposable representation of the series sl(1|n) and several individual Lie superalgebras. Partial results for other simple Lie superalgebras without Cartan matrix are reviewed. In particular, it is only for vect(0|2) and sh(0|4) that the typical irreducible representations can not participate in indecomposable modules; for other simple Lie superalgebras without Cartan matrix (of series vect(0|n), svect(0|n)$, svect(0|n)', spe(n) for n>2 and sh(0|m) for m>4) one can construct indecomposable representations with arbitrary composition factors. Several tame open problems are listed, among them a description of odd parameters
dc.description10 p., Latex
dc.identifierhttps://arxiv.org/abs/math/0202184
dc.identifierhttp://arxiv.org/abs/math/0202184
dc.identifierIn: A. N. Sissakian et. al. (ed.), {\em Memorial volume dedicated to Misha Saveliev and Igor Luzenko}, JINR, Dubna, 2000, 126--131
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/63374
dc.subjectRepresentation Theory
dc.subject17B10 (Primary) 16G20 (Secondary)
dc.titleIndecomposable representations of Lie superalgebras
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