Cohomology and deformation quantization of Poisson conformal algebras

Abstract

In this paper, we first recall the notion of (noncommutative) Poisson conformal algebras and give some constructions of them. Then 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.