Strongly r-matrix induced tensors, Koszul cohomology, and arbitrary-dimensional quadratic Poisson cohomology

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dc.creatorAmmar, Mourad
dc.creatorKass, Guy
dc.creatorMasmoudi, Mohsen
dc.creatorPoncin, Norbert
dc.date2007-08-21
dc.date.accessioned2026-07-07T08:24:42Z
dc.date.available2026-07-07T08:24:42Z
dc.descriptionWe introduce the concept of strongly $r$-matrix induced ({\small SRMI}) Poisson structure, report on the relation of this property with the stabilizer dimension of the considered quadratic Poisson tensor, and classify the Poisson structures of the Dufour-Haraki classification (DHC) according to their membership of the family of {\small SRMI} tensors. One of the main results of our work is a generic cohomological procedure for {\small SRMI} Poisson structures in arbitrary dimension. This approach allows decomposing Poisson cohomology into, basically, a Koszul cohomology and a relative cohomology. Moreover, we investigate this associated Koszul cohomology, highlight its tight connections with Spectral Theory, and reduce the computation of this main building block of Poisson cohomology to a problem of linear algebra. We apply these upshots to two structures of the DHC and provide an exhaustive description of their cohomology. We thus complete our list of data obtained in previous works, see \cite{MP} and \cite{AMPN}, and gain fairly good insight into the structure of Poisson cohomology.
dc.description25 pages
dc.identifierhttps://arxiv.org/abs/0708.2773
dc.identifierhttp://arxiv.org/abs/0708.2773
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/136430
dc.subjectSymplectic Geometry
dc.subject17B63; 17B56; 55N99
dc.titleStrongly r-matrix induced tensors, Koszul cohomology, and arbitrary-dimensional quadratic Poisson cohomology
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