$(G,\chi_{\phi})$-equivariant $\phi$-coordinated quasi modules for nonlocal vertex algebras

TL;DR

This paper develops a framework for $(G, ext{chi}_ ext{phi})$-equivariant $ ext{phi}$-coordinated quasi modules in nonlocal vertex algebras, introducing new formulas and constructions, and applies these to lattice vertex algebras.

Contribution

It introduces a generalized commutator formula and a construction method for weak quantum vertex algebras with equivariant modules, expanding the understanding of nonlocal vertex algebra modules.

Findings

Established a generalized commutator formula.

Constructed weak quantum vertex algebras with equivariant modules.

Applied the theory to lattice vertex algebras using twisted vertex operators.

Abstract

In this paper, we study $(G,\chi_{\phi})$-equivariant $\phi$-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 $(G,\chi_{\phi})$-equivariant $\phi$-coordinated quasi modules. As an application, we also construct (equivariant) $\phi$-coordinated quasi modules for lattice vertex algebras by using Lepowsky's work on twisted vertex operators.