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Communications in Mathematical Physics

, Volume 200, Issue 3, pp 545–560 | Cite as

Gerstenhaber Algebras and BV-Algebras in Poisson Geometry

Abstract:

The purpose of this paper is to establish an explicit correspondence between various geometric structures on a vector bundle with some well-known algebraic structures such as Gerstenhaber algebras and BV-algebras. Some applications are discussed. In particular, we find an explicit connection between the Koszul–Brylinski operator and the modular class of a Poisson manifold. As a consequence, we prove that Poisson homology is isomorphic to Poisson cohomology for unimodular Poisson structures.

Keywords

Manifold Vector Bundle Geometric Structure Algebraic Structure Poisson Structure 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Ping Xu
    • 1
  1. 1.Department of Mathematics, The Pennsylvania State University, University Park, PA 16802, USA.¶E-mail: ping@math.psu.eduUS

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