A generalization of twisted modules over vertex algebras

TL;DR

This paper generalizes the concept of twisted modules over vertex algebras by introducing (V,T)-modules for any positive integer T, and constructs associative algebras that classify simple modules.

Contribution

It introduces a new class of (V,T)-modules over vertex algebras for arbitrary T and establishes a correspondence with simple modules of associated associative algebras.

Findings

Constructed associative algebras A^{T}_{m}(V) for m in (1/T)N.

Established a one-to-one correspondence between simple modules of A^{T}_{0}(V) and simple (V,T)-modules.

Extended the framework of twisted modules to a more general setting.

Abstract

We introduce a notion of a (V,T)-module over a vertex algebra V for an arbitrary positive integer T, which is a generalization of a twisted V-module. Under some conditions on V, we construct an associative algebra A^{T}_{m}(V) for m\in(1/T)\N and an A^{T}_{m}(V)-A^{T}_{n}(V)-bimodule A^{T}_{n,m}(V) for n,m\in(1/T)\N and we establish a one-to-one correspondence between the set of isomorphism classes of simple left A^{T}_{0}(V)-modules and that of simple (1/T)\N-graded (V,T)-modules.