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

Abstract

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 $V^{\ast }[1]$. Fixed a universal deformation quantization (prediction some weights to all Kontsevich graphs [K97]), we have deformation quantization of the both algebras $S(V^{\ast })$ 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 Tamarkin's theory [T1].

49 pages, 2 figures

References in corpus (3)

• Kontsevich formality and PBW algebras
• An explicit construction of the Quillen homotopical category of dg Lie algebras
• Hochschild cohomology and derived Picard groups

Cited by in corpus (4)

• Hochschild cohomology and Atiyah classes
• Bimodules and branes in deformation quantization
• Operads, configuration spaces and quantization
• Deformation Quantization of A-infinity Equivalences