Journal of Noncommutative Geometry
Full-Text PDF (315 KB) | Metadata | Table of Contents | JNCG summary
Published online: 2015-10-29
Poisson and Hochschild cohomology and the semiclassical limitMatthew Towers (1) University of Kent at Canterbury, Canterbury, UK
Let $\mathsf A$ be a quantum algebra possessing a semiclassical limit $A$. We show that under certain hypotheses $\mathsf A^e$ can be thought of as a deformation of the Poisson enveloping algebra of $A$, and we give a criterion for the Hochschild cohomology of $\mathsf A$ to be a deformation of the Poisson cohomology of $A$ in the case that $\mathsf A$ 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.
Keywords: Poisson cohomology, Hochschild cohomology, semiclassical limit, Koszul algebra, deformations
Towers Matthew: Poisson and Hochschild cohomology and the semiclassical limit. J. Noncommut. Geom. 9 (2015), 665-696. doi: 10.4171/JNCG/204