# Universal enveloping Poisson conformal algebras

## TL;DR

This paper explores the connections between Poisson conformal algebras and Lie conformal algebra representations, providing explicit calculations for universal associative conformal envelopes of key algebraic structures.

## Contribution

It establishes new relations between Poisson and Lie conformal algebras and computes explicit brackets for universal conformal envelopes of Virasoro and Neveu-Schwarz algebras.

## Key findings

- Explicit Poisson brackets on graded conformal algebras
- Relations between Poisson conformal algebras and Lie conformal representations
- Calculations for universal associative conformal envelopes

## 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 Virasoro conformal algebra and Neveu--Schwartz conformal superalgebra.