$H_D$-Quantum Vertex Algebras

TL;DR

This paper introduces a new class of quantum vertex algebras where both commutativity and translation covariance are broken, characterized by braiding and translation maps, and satisfying a Braided Jacobi Identity.

Contribution

It defines and analyzes a novel class of quantum vertex algebras with broken translation covariance and a Braided Jacobi Identity, expanding the theoretical framework.

Findings

Defines a new class of quantum vertex algebras with braiding and translation maps.

Establishes the Braided Jacobi Identity for these algebras.

Provides foundational properties and potential applications.

Abstract

We discuss a class of quantum vertex algebras where not only the commutativity of the vertex algebra is broken by a braiding map $S^{(\tau)}$, but also the translation covariance is broken by a translation map $S^{(\gamma)}$. The new class of quantum vertex operators satisfy a Braided Jacobi Identity containing both the braiding and the translation maps.