Poisson and Hochschild cohomology and the semiclassical limit

Towers, Matthew (2013) Poisson and Hochschild cohomology and the semiclassical limit. arXiv, . (Full text available)

Abstract

Let $B$ be a quantum algebra possessing a semiclassical limit $A$. We show that under certain hypotheses $B^e$ can be thought of as a deformation of the Poisson enveloping algebra of $A$, and we give a criterion for the Hochschild cohomology of $B$ to be a deformation of the Poisson cohomology of $A$ in the case that $B$ is Koszul. We verify that condition for the algebra of $2\times 2$ quantum matrices and calculate its Hochschild cohomology and the Poisson cohomology of its semiclassical limit.

Item Type: Article
Additional information: Imported from arXiv
Subjects: Q Science > QA Mathematics (inc Computing science) > QA171 Representation theory
Divisions: Faculties > Sciences > School of Mathematics Statistics and Actuarial Science > Pure Mathematics
Depositing User: Matthew Towers
Date Deposited: 30 May 2014 10:49 UTC
Last Modified: 17 Jan 2017 20:49 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/41235 (The current URI for this page, for reference purposes)
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