On quantum vertex algebras and their modules

TL;DR

This paper surveys the development of quantum vertex algebras, detailing their conceptual construction, modules, and connections to double Yangians and Zamolodchikov-Faddeev algebras, highlighting recent theoretical advances.

Contribution

It provides a comprehensive overview of quantum vertex algebra theory, including new constructions and links to important algebraic structures.

Findings

Constructed quantum vertex algebras conceptually

Connected double Yangians with quantum vertex algebras

Linked Zamolodchikov-Faddeev algebras to quantum vertex algebras

Abstract

We give a survey on the developments in a certain theory of quantum vertex algebras, including a conceptual construction of quantum vertex algebras and their modules and a connection of double Yangians and Zamolodchikov-Faddeev algebras with quantum vertex algebras.