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


Author: Can Zhu
Journal: Proc. Amer. Math. Soc. 143 (2015), 1957-1967
MSC (2010): Primary 17B63, 18G60, 16S30
DOI: https://doi.org/10.1090/S0002-9939-2014-12411-7
Published electronically: December 19, 2014
MathSciNet review: 3314106
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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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Additional Information

Can Zhu
Affiliation: College of Science, University of Shanghai for Science and Technology, Shanghai 200093, People’s Republic of China
Email: czhu@usst.edu.cn

DOI: https://doi.org/10.1090/S0002-9939-2014-12411-7
Keywords: Affine Poisson algebra, Poisson (co)homology, Poincar\'e duality, enveloping algebra, Hochschild (co)homology
Received by editor(s): January 16, 2013
Received by editor(s) in revised form: November 14, 2013
Published electronically: December 19, 2014
Communicated by: Birge Huisgen-Zimmermann
Article copyright: © Copyright 2014 American Mathematical Society