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BV-algebra strucuture on Poisson cohomology Wu, Quanshui


Similar to the modular vector fields in Poisson geometry, modular derivations can be defined for smooth Poisson algebras with trivial canonical bundle. By twisting Poisson modules with the modular derivation, the Poisson cochain complex with values in any Poisson module is isomorphic to the Poisson chain complex with values in the corresponding twisted Poisson module. Then a version of twisted Poincar\'{e} duality is deduced between Poisson homologies and Poisson cohomologies. If the Poisson structure is pseudo-unimodular, then its Poisson cohomology as Gerstenhaber algebra is exact, that is, it has a Batalin-Vilkovisky algebra structure by using the isomorphism between the Poisson cochain complex and chain complex.

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