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

Lionel Richard (Edinburgh)

Wednesday 28th May, 2008 16:00-17:00 214


A classical problem in algebraic deformation is to compare the Poisson (co)homology of a Poisson algebra with the Hochschild (co)homology of its deformation. Although these homologies are known to behave similarly in smooth cases, the singular case seems more complicated to deal with. Our aim in this talk is to 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.

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