Associating quantum vertex algebras to Lie algebra ${\text{gl}}_{\mathrm{\infty }}$

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