Open AccessTwisted Poincaré duality for Poisson homology and cohomology of affine Poisson algebras
Author(s) -
Chen Zhu
Publication year - 2014
Publication title -
proceedings of the american mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.968
H-Index - 84
eISSN - 1088-6826
pISSN - 0002-9939
DOI - 10.1090/s0002-9939-2014-12411-7
Subject(s) - mathematics , cohomology , hochschild homology , pure mathematics , homology (biology) , poisson algebra , poisson distribution , poincaré duality , affine transformation , mayer–vietoris sequence , poisson bracket , poisson manifold , de rham cohomology , equivariant cohomology , symplectic geometry , lie algebra , chemistry , biochemistry , statistics , gene
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.