Cohomology and deformation quantization of Poisson conformal algebras

TL;DR

This paper explores the structure and deformation theory of Poisson conformal algebras, introducing cohomology to analyze their formal deformations and semi-classical limits.

Contribution

It develops a cohomology framework for noncommutative Poisson conformal algebras and links conformal formal deformations to their semi-classical limits.

Findings

Cohomology theory for noncommutative Poisson conformal algebras is established.

Poisson conformal algebras are shown to be semi-classical limits of conformal formal deformations.

New constructions of noncommutative Poisson conformal algebras are described.

Abstract

In this paper, we first recall the notion of (noncommutative) Poisson conformal algebras and describe some constructions of them. Then we study the formal distribution (noncommutative) Poisson algebras and coefficient (noncommutative) Poisson algebras. Next, we introduce the notion of conformal formal deformations of commutative associative conformal algebras and show that Poisson conformal algebras are the corresponding semi-classical limits. At last, we develop the cohomology theory of noncommutative Poisson conformal algebras and use this cohomology to study their deformations.