Fusion subcategories of representation categories of twisted quantum doubles of finite groups

Reconstructing Braided Subcategories of $SU(N)_k$

Ocneanu rigidity implies that there are finitely many (braided) fusion categories with a given set of fusion rules. While there is no method for determining all such categories up to equivalence, there are a few cases for which can. For example, Kazhdan and Wenzl described all fusion categories with fusion rules isomorphic to those of $SU(N)_k$. In this paper we extend their results to a statement about braided fusion categories, and obtain similar results for certain subcategories of $SU(N)_k$.

Existence of Tannakian subcategories and its applications

We study several classes of braided fusion categories, and prove that they all contain nontrivial Tannakian subcategories. As applications, we classify some fusion categories in terms of solvability and group-theoreticality.

Lagrangian subcategories and braided tensor equivalences of twisted quantum doubles of finite groups

We classify Lagrangian subcategories of the representation category of a twisted quantum double of a finite group. In view of results of 0704.0195v2 this gives a complete description of all braided tensor equivalent pairs of twisted quantum doubles of finite groups. We also establish a canonical bijection between Lagrangian subcategories of the representation category of a twisted quantum double of a finite group G and module categories over the category of twisted G-graded vector spaces such that the dual tensor category is pointed. This can be viewed as a quantum version of V. Drinfeld's cha…

Modular tensor categories, subcategories, and Galois orbits

We establish a set of general results to study how the Galois action on modular tensor categories interacts with fusion subcategories. This includes a characterization of fusion subcategories of modular tensor categories which are closed under the Galois action, and a classifcation of modular tensor categories which factor as a product of pointed and transitive categories in terms of pseudoinvertible objects. As an application, we classify modular tensor categories with two Galois orbits of simple objects and a nontrivial grading group.

商范畴的闭子范畴

Closed subcategories of quotient categories

本文研究了拟概形中闭子范畴的谱，并给出当$X$具有紧投射生成元集合时，用$X$中具有特殊性质的闭子范畴描述任意商范畴$X/Y$的闭子范畴的方法。

Equivariant fusion subcategories

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.