Equivariant fusion subcategories

TL;DR

This paper classifies all fusion subcategories within equivariantized fusion categories, offering new insights into their structure and applications to Hopf algebras and quantum doubles.

Contribution

It provides a comprehensive parameterization of fusion subcategories in equivariantization, extending understanding of their structure and applications.

Findings

Classified Hopf subalgebras of Kac-Paljutkin type Hopf algebras

Recovered classification of fusion subcategories of twisted quantum doubles

Established a general parameterization of fusion subcategories in equivariant categories

Abstract

We provide a parameterization of all fusion subcategories of the equivariantization by a group action on a fusion category. As applications, we classify the Hopf subalgebras of a family of semisimple Hopf algebras of Kac-Paljutkin type and recover Naidu-Nikshych-Witherspoon classification of the fusion subcategories of the representation category of a twisted quantum double of a finite group.