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Twisted Poincare duality for some quadratic Poisson algebras

S. Launois·L. Richard
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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.

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BibTeXRIS

S. Launois, L. Richard. 2006-11-23. Twisted Poincare duality for some quadratic Poisson algebras. https://doi.org/10.1007/s11005-006-0133-z

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