Noncommutative localization in smooth deformation quantization

TL;DR

This paper demonstrates the equivalence of algebraic and analytic localization methods in smooth deformation quantization, leveraging classical results from the theory of smooth function rings.

Contribution

It establishes the equivalence of algebraic and analytic localization in smooth deformation quantization, connecting modern quantization techniques with classical analysis.

Findings

Proves the equivalence of algebraic and analytic localization methods.

Utilizes classical results from Whitney, Malgrange, and Tougeron.

Applies to multiple situations in smooth deformation quantization.

Abstract

In this paper we shall show the equivalence of algebraic and analytic localisation for algebras of smooth deformation quantization for several situations. The proofs are based on old work by Whitney, Malgrange and Tougeron on the commutative algebra of smooth function rings from the 60's and 70's.