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تسجيل مستخدم جديدKoszul duality in deformation quantization and Tamarkins approach to Kontsevich formality
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تأليف
Boris Shoikhet
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Let $alpha$ be a quadratic Poisson bivector on a vector space $V$. Then one can also consider $alpha$ as a quadratic Poisson bivector on the vector space $V^*[1]$. Fixed a universal deformation quantization (prediction some weights to all Kontsevich graphs [K97]), we have deformation quantization of the both algebras $S(V^*)$ and $Lambda(V)$. These are graded quadratic algebras, and therefore Koszul algebras. We prove that for some universal deformation quantization, independent on $alpha$, these two algebras are Koszul dual. We characterize some deformation quantizations for which this theorem is true in the framework of the Tamarkins theory [T1].
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Let $alpha$ be a polynomial Poisson bivector on a finite-dimensional vector space $V$ over $mathbb{C}$. Then Kontsevich [K97] gives a formula for a quantization $fstar g$ of the algebra $S(V)^*$. We give a construction of an algebra with the PBW prop
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