$(G,{\chi }_{\varphi })$-equivariant $\varphi$-coordinated quasi modules for nonlocal vertex algebras

Abstract

In this paper, we study $(G,{\chi }_{\varphi })$-equivariant $\varphi$-coordinated quasi modules for nonlocal vertex algebras. Among the main results, we establish several conceptual results, including a generalized commutator formula and a general construction of weak quantum vertex algebras and their $(G,{\chi }_{\varphi })$-equivariant $\varphi$-coordinated quasi modules. As an application, we also construct (equivariant) $\varphi$-coordinated quasi modules for lattice vertex algebras by using Lepowsky's work on twisted vertex operators.