Remarks on $\phi$-coordinated modules for quantum vertex algebras

TL;DR

This paper explores $$-coordinated modules within weak quantum vertex algebras, establishing connections among different $$-modules and reinterpreting a key theorem for vertex operator algebras in this framework.

Contribution

It introduces new relationships among $$-coordinated modules and reinterprets existing theorems for vertex operator algebras using this perspective.

Findings

Established canonical connections among $$-coordinated modules for different $$

Reinterpreted Frenkel-Huang-Lepowsky's theorem in terms of $$-coordinated modules

Enhanced understanding of module structures in quantum vertex algebras

Abstract

This paper is about $\phi$-coordinated modules for weak quantum vertex algebras. Among the main results, several canonical connections among $\phi$-coordinated modules for different $\phi$ are established. For vertex operator algebras, a reinterpretation of Frenkel-Huang-Lepowsky's theorem on contragredient module is given in terms of $\phi$-coordinated modules.