Poisson (co)homology of truncated polynomial algebras in two variables

TL;DR

This paper investigates the Poisson (co)homology of truncated polynomial algebras in two variables, revealing an isomorphism with the Hochschild cohomology of related quantum algebras, bridging classical and quantum algebraic structures.

Contribution

It establishes an isomorphism between Poisson cohomology and Hochschild cohomology for truncated polynomial algebras and quantum complete intersections.

Findings

Poisson cohomology ring is isomorphic to Hochschild cohomology ring.

Provides a link between classical Poisson structures and quantum algebra.

Enhances understanding of algebraic structures in semi-classical limits.

Abstract

We study the Poisson (co)homology of the algebra of truncated polynomials in two variables viewed as the semi-classical limit of a quantum complete intersection studied by Bergh and Erdmann. We show in particular that the Poisson cohomology ring of such a Poisson algebra is isomorphic to the Hochschild cohomology ring of the corresponding quantum complete intersection.