Associating quantum vertex algebras to Lie algebra $\gl_{\infty}$

TL;DR

This paper establishes a canonical link between quantum vertex algebras and the Lie algebra gl_{} with its central extension, using an auxiliary infinite-dimensional Lie algebra for construction.

Contribution

It introduces a new method to associate quantum vertex algebras to gl_{} and its extension, expanding the understanding of their algebraic structures.

Findings

Constructed a canonical association between quantum vertex algebras and gl_{}

Developed a related infinite-dimensional Lie algebra for the construction

Provided a framework for gl_{} modules in quantum algebra context

Abstract

In this paper, we present a canonical association of quantum vertex algebras and their $\phi$-coordinated modules to Lie algebra $\gl_{\infty}$ and its 1-dimensional central extension. To this end we construct and make use of another closely related infinite-dimensional Lie algebra.