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Cohomology of Koszul-Vinberg algebroids and Poisson manifolds, I

Volume 54 / 2001

Michel Nguiffo Boyom Banach Center Publications 54 (2001), 99-110 MSC: Primary 22A22, 53B05, 53C12, 53D17; Secondary 17B55, 17B63. DOI: 10.4064/bc54-0-7

Abstract

We introduce a cohomology theory of Koszul-Vinberg algebroids. The relationships between that cohomology and Poisson manifolds are investigated. We focus on the complex of chains of superorders [KJL1]. We prove that symbols of some sort of cycles give rise to so called bundlelike Poisson structures. In particular we show that if $E\rightarrow M$ is a transitive Koszul-Vinberg algebroid whose anchor is injective then a Koszul-Vinberg cocycle $\theta$ whose symbol has non-zero skew symmetric component defines a transversally Poissonian symplectic foliation in % $M$.

Authors

  • Michel Nguiffo BoyomUMR 5030 CNRS
    Département de Mathématiques
    Université Montpellier 2
    34095 Montpellier Cedex 5, France
    e-mail

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