Formal Poisson cohomology of twisted $r$-matrix induced structures

Simple item page
dc.creatorAmmar, Mourad
dc.creatorPoncin, Norbert
dc.date2006-10-04
dc.date.accessioned2026-07-07T07:28:42Z
dc.date.available2026-07-07T07:28:42Z
dc.descriptionQuadratic Poisson tensors of the Dufour-Haraki classification read as a sum of an $r$-matrix induced structure twisted by a (small) compatible exact quadratic tensor. An appropriate bigrading of the space of formal Poisson cochains then leads to a vertically positive double complex. The associated spectral sequence allows to compute the Poisson-Lichnerowicz cohomology of the considered tensors. We depict this modus operandi, apply our technique to concrete examples of twisted Poisson structures, and obtain a complete description of their cohomology. As richness of Poisson cohomology entails computation through the whole spectral sequence, we detail an entire model of this sequence. Finally, the paper provides practical insight into the operating mode of spectral sequences.
dc.description20 pages
dc.identifierhttps://arxiv.org/abs/math/0610152
dc.identifierhttp://arxiv.org/abs/math/0610152
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/117829
dc.subjectSymplectic Geometry
dc.subject17B63; 17B56; 55T05
dc.titleFormal Poisson cohomology of twisted $r$-matrix induced structures
dc.typetext

Files

Collections

arXiv