Poisson Equivalence over a Symplectic Leaf

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dc.creatorVorobjev, Yurii
dc.date2005-03-28
dc.date2005-06-11
dc.date.accessioned2026-07-07T05:18:32Z
dc.date.available2026-07-07T05:18:32Z
dc.descriptionWe study the equivalence of Poisson structures around a given symplectic leaf of nonzero dimension. Some criteria of Poisson equivalence are derived from a homotopy argument for coupling Poisson structures. In the case when the transverse Lie algebra of the symplectic leaf is semisimple of compact type, we show that an obstruction to the linearizability is the cohomology class of a Casimir 2-cocycle. This allows us to obtain a semilocal analog of the Conn linearization theorem and to clarify examples of nonlinearizable Poisson structures due to \cite{DW}.
dc.descriptionLatex file, 52p, minor corrections
dc.identifierhttps://arxiv.org/abs/math/0503628
dc.identifierhttp://arxiv.org/abs/math/0503628
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/74695
dc.subjectSymplectic Geometry
dc.subject53D17, 53C05
dc.titlePoisson Equivalence over a Symplectic Leaf
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