Twisted Heisenberg-Virasoro vertex operator algebra

TL;DR

This paper introduces a new vertex operator algebra linked to the twisted Heisenberg-Virasoro algebra, exploring its structure, modules, and relationships with other algebra categories, and solving the commutant problem.

Contribution

It characterizes the twisted Heisenberg-Virasoro vertex operator algebra as a tensor product and analyzes its module categories and commutant structure.

Findings

Established the algebra's structure as a tensor product of known VOAs.

Analyzed the module categories of twisted Heisenberg-Virasoro algebras.

Solved the commutant problem for this algebra.

Abstract

In this paper, we study a new kind of vertex operator algebra related to the twisted Heisenberg-Virasoro algebra, which we call the twisted Heisenberg-Virasoro vertex operator algebra, and its modules. Specifically, we present some results concerning the relationship between the restricted module categories of twisted Heisenberg-Virasoro algebras of rank one and rank two and several different kinds of module categories of their corresponding vertex algebras. We also study fully the structures of the twisted Heisenberg-Virasoro vertex operator algebra, give a characterization of it as a tensor product of two well-known vertex operator algebras, and solve the commutant problem.