# On the structure of quantum vertex algebras

## TL;DR

This paper develops a structure theory for quantum vertex algebras, a deformation of vertex algebras, introducing braided n-products and proving a Borcherds identity analogue.

## Contribution

It extends the theory of vertex algebras by formulating a structure framework for quantum vertex algebras, including new algebraic identities.

## Key findings

- Introduction of braided n-products
- Proof of a Borcherds identity analogue
- Parallel development to classical vertex algebra theory

## Abstract

A definition of a quantum vertex algebra, which is a deformation of a vertex algebra, was proposed by Etingof and Kazhdan in 1998. In a nutshell, a quantum vertex algebra is a braided state-field correspondence which satisfies associativity and braided locality axioms. We develop a structure theory of quantum vertex algebras, parallel to that of vertex algebras. In particular, we introduce braided n-products for a braided state-field correspondence and prove for quantum vertex algebras a version of the Borcherds identity.