Twisted representations of vertex operator algebras associated to affine Lie algebras

TL;DR

This paper proves the semisimplicity of categories of lower bounded twisted modules for vertex operator algebras linked to affine Lie algebras, using a twisted Zhu's algebra generalization, and establishes their equivalence under automorphisms.

Contribution

It introduces a twisted Zhu's algebra framework to analyze module categories and shows their equivalence under automorphisms, advancing understanding of vertex operator algebra representations.

Findings

Categories of twisted modules are semisimple.

Equivalence of module categories under automorphisms.

Extension of Zhu's algebra to twisted cases.

Abstract

In this paper, we prove the categories of lower bounded twisted modules of positive integer levels for simple vertex operator algebras associated with affine Lie algebras and general automorphisms are semisimple, using the twisted generalization of Zhu's algebra for these vertex operator algebras, constructed in \cite{HY}. We also show that the category of lower bounded twisted modules for a general automorphism is equivalent to the category of lower bounded twisted modules for the corresponding diagram automorphism.