Generalized inversion of the Hochschild coboundary operator and deformation quantization

TL;DR

This paper introduces a generalized inverse of the Hochschild coboundary operator, enabling systematic computation of star products on Poisson manifolds, which advances deformation quantization techniques.

Contribution

It defines a new generalized inverse of the Hochschild coboundary operator using derivative decomposition, facilitating calculations in deformation quantization.

Findings

Enables systematic computation of star products

Provides a new method for deformation quantization

Advances mathematical tools for Poisson manifolds

Abstract

Using a derivative decomposition of the Hochschild differential complex we define a generalized inverse of the Hochschild coboundary operator. It can be applied for systematic computations of star products on Poisson manifolds.