Module categories over finite pointed tensor categories

TL;DR

This paper classifies exact module categories over certain finite pointed tensor categories, providing a deeper understanding of their structure and representation theory in the context of finite-dimensional quasi-Hopf algebras.

Contribution

It offers a classification of exact module categories over specific pointed tensor categories with cyclic groups of invertible objects, advancing the understanding of their module category structure.

Findings

Classified exact module categories over some pointed tensor categories

Connected module categories to the structure of finite-dimensional quasi-Hopf algebras

Enhanced understanding of representation categories of finite groups

Abstract

We study exact module categories over the representation categories of finite-dimensional quasi-Hopf algebras. As a consequence we classify exact module categories over some families of pointed tensor categories with cyclic group of invertible objets of order p, where p is a prime number.