Koszul duality in deformation quantization and Tamarkin's approach to Kontsevich formality |
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Authors: | Boris Shoikhet |
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Institution: | Faculty of Science, Technology and Communication, Campus Limpertsberg, University of Luxembourg, 162A avenue de la Faiencerie, L-1511 Luxembourg |
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Abstract: | Let α be a quadratic Poisson bivector on a vector space V. Then one can also consider α as a quadratic Poisson bivector on the vector space V∗1]. Fixed a universal deformation quantization (prediction of some complex weights to all Kontsevich graphs 12]), we have deformation quantization of the both algebras S(V∗) and Λ(V). These are graded quadratic algebras, and therefore Koszul algebras. We prove that for some universal deformation quantization, independent on α, these two algebras are Koszul dual. We characterize some deformation quantizations for which this theorem is true in the framework of the Tamarkin's theory 19]. |
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Keywords: | Deformation quantization Koszul duality Operad theory |
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