Deformation quantization with generators and relations

Abstract

In this paper we prove a conjecture of B. Shoikhet which claims that two quantization procedures arising from Fourier dual constructions actually coincide.

9 pages; 4 figures; many typos have been corrected; the introduction has been considerably extended and a more detailed exposition of the Koszul theory behind the main idea has been added; the proof of Proposition 2.4 (iii) has been also extended; Subsection 3.2 has been enlarged, and a more detailed exposition of how the Duflo element arises has been added

References in corpus (4)

• A Counterexample to the Quantizability of Modules
• Bimodules and branes in deformation quantization
• Biquantization of symmetric pairs and the quantum shift
• Kontsevich formality and PBW algebras

Cited by in corpus (6)

• "Quantization is a mystery"
• A note on the Koszul complex in deformation quantization
• On the compatibility between cup products, the Alekseev--Torossian connection and the Kashiwara--Vergne conjecture
• The explicit equivalence between the standard and the logarithmic star product for Lie algebras
• Characteristic classes in deformation quantization
• The Chevalley--Eilenberg complex and deformation quantization in presence of two branes