$${\phi}$$ -Coordinated Quasi-Modules for Quantum Vertex Algebras

Abstract

We develop a theory of \({\phi}\) -coordinated (quasi-) modules for a general nonlocal vertex algebra where \({\phi}\) is what we call an associate of the one-dimensional additive formal group. By specializing \({\phi}\) to a particular associate, we obtain a new construction of weak quantum vertex algebras in the sense of Li (Selecta Mathematica (New Series) 11:349–397, 2005). As an application, we associate weak quantum vertex algebras to quantum affine algebras, and we also associate quantum vertex algebras and \({\phi}\) -coordinated modules to a certain quantum βγ-system explicitly.