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.
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Received: 19 January 1998 / Accepted: 27 July 1998
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Xu, P. Gerstenhaber Algebras and BV-Algebras in Poisson Geometry. Comm Math Phys 200, 545–560 (1999). https://doi.org/10.1007/s002200050540
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DOI: https://doi.org/10.1007/s002200050540