# Twisted Poincare duality for some quadratic Poisson algebras

Launois, Stephane, Richard, Lionel (2007) Twisted Poincare duality for some quadratic Poisson algebras. Letters in Mathematical Physics, 79 (2). pp. 161-174. ISSN 0377-9017. (doi:10.1007/s11005-006-0133-z)

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## Abstract

We exhibit a Poisson module restoring a twisted Poincaré duality between Poisson homology and cohomology for the polynomial algebra R=C[X1Xn] endowed with Poisson bracket arising from a uniparametrised quantum affine space. This Poisson module is obtained as the semiclassical limit of the dualising bimodule for Hochschild homology of the corresponding quantum affine space. As a corollary we compute the Poisson cohomology of R, and so retrieve a result obtained by direct methods (so completely different from ours) by Monnier.

Item Type: Article 10.1007/s11005-006-0133-z Poisson (co)homology - Hochschild (co)homology - Poincaré duality Q Science > QA Mathematics (inc Computing science) Faculties > Sciences > School of Mathematics Statistics and Actuarial ScienceFaculties > Sciences > School of Mathematics Statistics and Actuarial Science > Pure Mathematics Stephane Launois 03 Jun 2008 14:28 UTC 28 May 2019 13:38 UTC https://kar.kent.ac.uk/id/eprint/3154 (The current URI for this page, for reference purposes)