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 found an explicit connection between the Koszul-Brylinski operator of a Poisson manifold and its modular class. As a consequence, we prove that Poisson homology is isomorphic to Poisson cohomology for unimodular Poisson structures.

18 pages, LaTeX

References in corpus (1)

• The outer derivation of a complex Poisson manifold

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