Gerstenhaber algebras and BV-algebras in Poisson geometry

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105 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)545-560
Number of pages16
JournalCommunications In Mathematical Physics
Issue number3
StatePublished - 1999

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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