On associative algebras, modules and twisted modules for vertex operator algebras

TL;DR

This paper introduces a new functor construction linking associative algebra modules to admissible modules in vertex operator algebras, enabling analysis without relying on the commutator formula.

Contribution

It presents a novel method for constructing functors from associative algebra modules to admissible modules in vertex operator algebras, applicable even without the commutator formula.

Findings

New functor construction for modules and twisted modules

Method applicable without the commutator formula

Enhances understanding of module categories in vertex operator algebras

Abstract

We give a new construction of functors from the category of modules for the associative algebras $A_n(V)$ and $A_g(V)$ associated with a vertex operator algebra $V$, defined by Dong, Li and Mason, to the category of admissible $V$-modules and admissible twisted $V$-modules, respectively, using the method developed in the joint work \cite{HY1} with Y.-Z. Huang. The functors were first constructed by Dong, Li and Mason, but the importance of the new method, as in \cite{HY1}, is that we can apply the method to study objects without the commutator formula in the representation theory of vertex operator algebras.