On global deformation quantization in the algebraic case

TL;DR

This paper provides a new proof of a global algebraic deformation quantization result that avoids local section choices by leveraging algebraic De Rham cohomology techniques.

Contribution

It introduces a novel proof method for Yekutieli's global algebraic deformation quantization, simplifying the approach by using algebraic De Rham cohomology.

Findings

Proof of Yekutieli's result without local section choices

Application of algebraic De Rham cohomology in deformation quantization

Simplified and more general proof technique

Abstract

We give a proof of Yekutieli's global algebraic deformation quantization result which does not rely on the choice of local sections of the bundle of affine coordinate systems. Instead we use an argument inspired by algebraic De Rham cohomology.