Twisted Poincaré duality for Poisson homology and cohomology of affine Poisson algebras

Zhu, Can

doi:10.1090/S0002-9939-2014-12411-7

Twisted Poincaré duality for Poisson homology and cohomology of affine Poisson algebras
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Proc. Amer. Math. Soc. 143 (2015), 1957-1967 Request permission

Abstract:

This paper investigates the Poisson (co)homology of affine Poisson algebras. It is shown that there is a twisted Poincaré duality between their Poisson homology and cohomology. The relation between the Poisson (co)homology of an affine Poisson algebra and the Hochschild (co)homology of its deformation quantization is also discussed, which is similar to Kassel’s result (1988) for homology and is a special case of Kontsevich’s theorem (2003) for cohomology.

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