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Article Dans Une Revue Compositio Mathematica Année : 2011

Bimodules and branes in deformation quantization

Résumé

We prove a version of Kontsevich's formality theorem for two subspaces (branes) of a vector space $X$. The result implies in particular that the Kontsevich deformation quantizations of $\mathrm{S}(X^*)$ and $\wedge(X)$ associated with a quadratic Poisson structure are Koszul dual. This answers an open question in Shoikhet's recent paper on Koszul duality in deformation quantization.

Dates et versions

hal-00410600 , version 1 (21-08-2009)

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Damien Calaque, Giovanni Felder, Andrea Ferrario, Carlo A. Rossi. Bimodules and branes in deformation quantization. Compositio Mathematica, 2011, 147, pp.105-160. ⟨10.1112/S0010437X10004847⟩. ⟨hal-00410600⟩
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