Twisted Poincare duality for some quadratic Poisson algebras

Details Twisted Poincare duality for some quadratic Poisson algebras Twisted Poincare duality for some quadratic Poisson algebras

2006-09-14

arxiv.org/abs/math/0609390v3

Letters in Mathematical Physics, 79 (2), 2007, 161-174

Mathematics

K-Theory and Homology

17 pages. Few misprints corrected in the new version

Scientific paper

10.1007/s11005-006-0133-z

We exhibit a Poisson module restoring a twisted Poincare duality between Poisson homology and cohomology for the polynomial algebra R=C[X_1,...,X_n] 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.

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