Weight-one elements of vertex operator algebras and automorphisms of categories of generalized twisted modules

TL;DR

This paper constructs automorphisms of categories of generalized twisted modules in vertex operator algebras using weight-one elements, with explicit applications to affine VOAs and Lie algebra automorphisms.

Contribution

It introduces a novel method to generate automorphisms of module categories from weight-one elements in VOAs, especially for affine VOAs.

Findings

Explicit automorphisms of module categories for affine VOAs.

Construction of generalized twisted modules from Lie algebra automorphisms.

Connections between twisted modules and diagram automorphisms.

Abstract

Given a weight-one element $u$ of a vertex operator algebra $V$, we construct an automorphism of the category of generalized $g$-twisted modules for automorphisms $g$ of $V$ fixing $u$. We apply this construction to the case that $V$ is an affine vertex operator algebra to obtain explicit results on these automorphisms of categories. In particular, we give explicit constructions of certain generalized twisted modules from generalized twisted modules associated to diagram automorphisms of finite-dimensional simple Lie algebras and generalized (untwisted) modules.