An approach to the tangential Poisson cohomology based on examples in duals of Lie algebras

Angela Gammella

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An approach to the tangential Poisson cohomology based on examples in duals of Lie algebras

Angela Gammella

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Abstract

We study the tangential Poisson cohomology (TP-cohomology) of regular Poisson manifolds, first defined by Lichnerowicz using contravariant tensor fields. We show that for a regular Poisson manifold M, the TP-cohomology coincides with the leafwise de Rham (or Cech) cohomology of the symplectic foliation of M. Its computation in various degrees leads to open, non trivial problems. To get a better understanding of these difficulties, we study explicitly many examples coming from nilpotent and 3-dimensional (real) Lie algebras. For the latter, we compare the TP-cohomology and the usual Poisson cohomology (P-cohomology).

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BibTeX RIS

Angela Gammella. 2002-07-27. An approach to the tangential Poisson cohomology based on examples in duals of Lie algebras. https://arxiv.org/abs/math/0207215

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