# Generalized Twisted Quantum Doubles of a Finite Group and Rational Orbifolds

## TL;DR

This paper explores the connection between certain modular quasi-Hopf algebras derived from finite groups and the orbifold models of rational vertex operator algebras, expanding the understanding of their module categories.

## Contribution

It provides a new description of orbifold models of rational vertex operator algebras whose module categories are tensor equivalent to generalized twisted quantum doubles.

## Key findings

- Characterization of orbifold models via $D^{ ext{omega}}(G, A)$-module categories
- Extension of quasi-Hopf algebra theory to orbifold constructions
- Framework for analyzing rational vertex operator algebra modules

## Abstract

In previous work the authors introduced a new class of modular quasi-Hopf algebras $D^{\omega}(G, A)$ associated to a finite group $G$, a central subgroup $A$, and a $3$-cocycle $\omega\in Z^3(G, C^x)$. In the present paper we propose a description of the class of orbifold models of rational vertex operator algebras whose module category is tensor equivalent to $D^{\omega}(G, A)$-mod. The paper includes background on quasi-Hopf algebras and a discussion of some relevant orbifolds.