2002/03/14 by Michel Nguiffo Boyom, Boyom, Michel Nguiffo
Mathematics · #Advanced Topics in Algebra #Algebra over a field #Algebraic structures and combinatorial models #Differential Geometry (math.DG) #FOS: Mathematics #Holomorphic and Operator Theory #Holomorphic function #Homology (biology) #Homotopy and Cohomology in Algebraic Topology #Lie algebra #Mathematics #Poisson algebra #Poisson bracket #Poisson distribution #Poisson manifold #Pure mathematics #Symplectic geometry #math.DG
paper · pdf · doi:10.48550/arxiv.math/0203135
arxiv created 2002/03/14 · openalex publication_date 2002/03/14 · arxiv updated 2016/09/07 · openalex created_date 2022/10/01 · openalex updated_date 2026/08/05
We deal with smooth real manifolds as well as complex analytic manifolds as\nwell. It is well known that the concept of star product is powerful enough to\nproduce all Poisson structures on real manifolds. According to [BdM] it is not\nknown whether holomorphic star products exist on complex analytic manifolds.\n The main purpose of this paper is to show that the concept of homology of\nKoszul-Vinberg algebroids on smooth (resp. complex analytic) manifolds is an\neffective tool to produce smooth (resp complex analytic) Poisson structures on\nsmooth (resp. complex analytic) manifolds. We also study some invariants of\ncontact structures which arise from the associated Koszul-Vinberg algebroids.\n