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arXiv · 0805.0174

Koszul duality in deformation quantization and Tamarkin's approach to Kontsevich formality

Boris Shoikhet
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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 some weights to all Kontsevich graphs [K97]), 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 [T1].

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Boris Shoikhet. 2009-09-26. Koszul duality in deformation quantization and Tamarkin's approach to Kontsevich formality. https://arxiv.org/abs/0805.0174

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