Filtering bases and cohomology of nilpotent subalgebras of Witt and $\widetilde{sl}_2$ Lie algebras

dc.creatorWeinstein, F. V.
dc.date2006-04-28
dc.date2006-05-05
dc.date.accessioned2026-07-07T07:11:22Z
dc.date.available2026-07-07T07:11:22Z
dc.descriptionWe study the cohomology with trivial coefficients of Lie algebras L_k of the polynomial vector fields on the line with zero $k$-jet, (k>=1), and the cohomology of the similar subalgebras {L}_k of the polynomial loops algebra $\widetilde{sl}_2$. In both cases we construct the special bases (filtering bases) in the external complexes of these algebras. A spectral sequence based on this construction allows to completely find the cohomology of L_k and {L}_k. We also apply the filtering bases to find the spectral resolution of the Laplace operators for algebras L_1 and L_0, and obtain explicit formulas for the representing cycles of homologies for algebras L_k and {L}_k by means of the Schur polynomials.
dc.description21 pages
dc.identifierhttps://arxiv.org/abs/math/0604631
dc.identifierhttp://arxiv.org/abs/math/0604631
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/111729
dc.subjectRepresentation Theory
dc.subjectCombinatorics
dc.subject17B68
dc.titleFiltering bases and cohomology of nilpotent subalgebras of Witt and $\widetilde{sl}_2$ Lie algebras
dc.typetext

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