Twisted regular representations and bimodules in vertex operator algebra theory

TL;DR

This paper extends the theory of vertex operator algebras by constructing bimodules using twisted regular representations and confirms a conjecture related to bimodule theory, advancing the understanding of algebraic structures in this field.

Contribution

It introduces a method to construct bimodules over twisted Zhu algebras using twisted regular representations, extending previous work and confirming a key conjecture.

Findings

Construction of bimodules over twisted Zhu algebras

Extension of Li's work to twisted cases

Confirmation of Dong and Jiang's bimodule conjecture

Abstract

In this paper, we use the twisted regular representation theory of vertex operator algebras to construct bimodules over twisted Zhu algebras, extending Haisheng Li's work in untwisted scenarios. Moreover, a conjecture of Dong and Jiang on bimodule theory is confirmed.