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Carlo Rossi, Instituto Superior Técnico

Deformation quantization via generators and relations

We prove a conjecture of B.Shoikhet, relating the (standard) deformation quantization of the symmetric algebra of a finite-dimensional vector field (over a closed field $k$ containing $C$) of Kontsevich, and a less standard one in terms of generators and relations. The key-point lies in the fact that Koszul duality is “preserved” (in a suitable sense) by deformation quantization.