Deformation quantization with generators and relations

TL;DR

This paper proves a conjecture that two different deformation quantization procedures, based on Fourier duality, are actually equivalent, clarifying the relationship between these approaches in mathematical physics.

Contribution

It confirms Shoikhet's conjecture, demonstrating the equivalence of two Fourier dual-based deformation quantization methods.

Findings

Two quantization procedures from Fourier dual constructions coincide

The proof resolves a conjecture in deformation quantization

Clarifies the relationship between different quantization approaches

Abstract

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