Twisted Poincare duality for some quadratic Poisson algebras
K-Theory and Homology
2007-06-13 v3 Differential Geometry
Quantum Algebra
Rings and Algebras
Abstract
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.
Keywords
Cite
@article{arxiv.math/0609390,
title = {Twisted Poincare duality for some quadratic Poisson algebras},
author = {S. Launois and L. Richard},
journal= {arXiv preprint arXiv:math/0609390},
year = {2007}
}
Comments
17 pages. Few misprints corrected in the new version