Graded filiform Lie algebras and symplectic nilmanifolds

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dc.creatorMillionschikov, Dmitri V.
dc.date2002-05-06
dc.date.accessioned2026-07-07T04:48:16Z
dc.date.available2026-07-07T04:48:16Z
dc.descriptionWe study symplectic (contact) structures on nilmanifolds that correspond to the filiform Lie algebras - nilpotent Lie algebras of the maximal length of the descending central sequence. We give a complete classification of filiform Lie algebras that possess a basis e_1, ..., e_n, [e_i,e_j]=c_{ij}e_{i{+}j} (N-graded Lie algebras). In particular we describe the spaces of symplectic cohomology classes for all even-dimensional algebras of the list. It is proved that a symplectic filiform Lie algebra is a filtered deformation of some N-graded symplectic filiform Lie algebra. But this condition is not sufficient. A spectral sequence is constructed in order to answer the question whether a given deformation of a N-graded symplectic filiform Lie algebra admits a symplectic structure or not. Other applications and examples are discussed.
dc.description20 pages
dc.identifierhttps://arxiv.org/abs/math/0205042
dc.identifierhttp://arxiv.org/abs/math/0205042
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/63980
dc.subjectRings and Algebras
dc.subjectDifferential Geometry
dc.subjectSymplectic Geometry
dc.subject17B30, 17B56, 17B70, 53D
dc.titleGraded filiform Lie algebras and symplectic nilmanifolds
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