Universal enveloping Poisson conformal algebras

Abstract

Lie conformal algebras are useful tools for studying vertex operator algebras and their representations. In this paper, we establish close relations between Poisson conformal algebras and representations of Lie conformal algebras. We also calculate explicitly Poisson conformal brackets on the associated graded conformal algebras of universal associative conformal envelopes of the Virasoro conformal algebra and the Neveu–Schwartz conformal superalgebra.