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) (KAR id:3154)

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Official URL: http://dx.doi.org/10.1007/s11005-006-0133-z

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
DOI/Identification number:	10.1007/s11005-006-0133-z
Uncontrolled keywords:	Poisson (co)homology - Hochschild (co)homology - Poincaré duality
Subjects:	Q Science > QA Mathematics (inc Computing science)
Institutional Unit:	Schools > School of Engineering, Mathematics and Physics > Mathematical Sciences
Former Institutional Unit:	Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science
Depositing User:	Stephane Launois
Date Deposited:	03 Jun 2008 14:28 UTC
Last Modified:	20 May 2025 11:30 UTC
Resource URI:	https://kar.kent.ac.uk/id/eprint/3154 (The current URI for this page, for reference purposes)

University of Kent Author Information

Launois, Stephane.

Creator's ORCID:	https://orcid.org/0000-0001-7252-8515
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