Defining relations for classical Lie superalgebras without Cartan matrices

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dc.creatorGrozman, Pavel
dc.creatorLeites, Dimitry
dc.creatorPoletaeva, Elena
dc.date2002-02-18
dc.date.accessioned2026-07-07T06:20:00Z
dc.date.available2026-07-07T06:20:00Z
dc.descriptionThe analogs of Chevalley generators are offered for simple (and close to them) Z-graded complex Lie algebras and Lie superalgebras of polynomial growth without Cartan matrix. We show how to derive the defining relations between these generators and explicitly write them for a "most natural" ("distinguished" in terms of Penkov and Serganova) system of simple roots. The results are given mainly for Lie superalgebras whose component of degree zero is a Lie algebra (other cases being left to the reader). Observe presentations of exceptional Lie superalgebras and Lie superalgebras of hamiltonian vector fields. Now we can, at last, q-quantize the Lie Lie superalgebras of hamiltonian vector fields and Poisson superalgebras.
dc.description13p., Latex (this is an expanded version of the SQS'99 talk)
dc.identifierhttps://arxiv.org/abs/math/0202152
dc.identifierhttp://arxiv.org/abs/math/0202152
dc.identifierIn: E. Ivanov et. al. (eds.) Supersymmetries and Quantum Symmetries (SQS'99, 27--31 July, 1999), Dubna, JINR, 2000, 387--396; Homology, Homotopy and Applications, v 4(2), 2002, 259-275
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/95220
dc.subjectRepresentation Theory
dc.subject17B10 (Primary) 17B65, 33C45, 33C80 (Secondary)
dc.titleDefining relations for classical Lie superalgebras without Cartan matrices
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