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

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