相关论文: Rank-finiteness for G-crossed braided fusion categ…

For a finite group $G$, a $G$-crossed braided fusion category is $G$-graded fusion category with additional structures, namely a $G$-action and a $G$-braiding. We develop the notion of $G$-crossed braided zesting: an explicit method for…

We give a short proof for a well-known formula for the rank of a $G$-crossed braided extension of a modular tensor category.

In this paper we study the relative tensor product of module categories over braided fusion categories using, in part, the notion of the relative center of a module category. In particular we investigate the canonical tensor category…

We show that braidings on a fusion category $\mathcal{C}$ correspond to certain fusion subcategories of the center of $\mathcal{C}$ transversal to the canonical Lagrangian algebra. This allows to classify braidings on non-degenerate and…

For a braided fusion category $\mathcal{V}$, a $\mathcal{V}$-fusion category is a fusion category $\mathcal{C}$ equipped with a braided monoidal functor $\mathcal{F}:\mathcal{V} \to Z(\mathcal{C})$. Given a fixed $\mathcal{V}$-fusion…

In this paper, we study fusion categories which contain a proper fusion subcategory with maximal rank. They can be viewed as generalizations of near-group fusion categories. We first prove that they admit spherical structure. We then…

We introduce, for a symmetric fusion category $\mathcal{A}$ with Drinfeld centre $\mathcal{Z}(\mathcal{A})$, the notion of $\mathcal{Z}(\mathcal{A})$-crossed braided tensor category. These are categories that are enriched over…

This work is a detailed version of arXiv:0704.0195 [math.QA]. We introduce a new notion of the core of a braided fusion category. It allows to separate the part of a braided fusion category that does not come from finite groups. We also…

We introduce a finiteness property for braided fusion categories, describe a conjecture that would characterize categories possessing this, and verify the conjecture in a number of important cases. In particular we say a category has F if…

In this paper, we study the structure of a generalized near-group fusion category and classified it when it is slightly degenerate.

We use a 2-categorical version of (de-)equivariantization to classify (3+1)d topological orders with a finite $G$-symmetry. In particular, we argue that (3+1)d fermionic topological order with $G$-symmetry correspond to…

We describe the structure of a generalized near-group fusion category and present an example of this class of fusion categories which arises from the extension of a Fibonacci category. We then classify slightly degenerate generalized…

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.

We classify braided extensions $C$ of a rank $2$ fusion category. The result shows that $C$ is tensor equivalent to a Deligne's tensor product of some known categories, except $C$ is slightly degenerate and generated by a…

The feasibility of a classification-by-rank program for modular categories follows from the Rank-Finiteness Theorem. We develop arithmetic, representation theoretic and algebraic methods for classifying modular categories by rank. As an…

Let C be a fusion category faithfully graded by a finite group G and let D be the trivial component of this grading. The center Z(C) of C is shown to be canonically equivalent to a G-equivariantization of the relative center Z_D(C). We use…

We give a rigorous development of the construction of new braided fusion categories from a given category known as zesting. This method has been used in the past to provide categorifications of new fusion rule algebras, modular data, and…

We provide a general formula for Mueger's centralizer of any fusion subcategory of a braided fusion category containing a tannakian subcategory. This entails a description for Mueger's centralizer of all fusion subcategories of a group…

A braided fusion category is said to have Property $\textbf{F}$ if the associated braid group representations factor over a finite group. We verify integral metaplectic modular categories have property $\textbf{F}$ by showing these…

For a finite braided tensor category we introduce its Picard crossed module consisting of the group of invertible module categories and the group of braided tensor autoequivalences. We describe the Picard crossed module in terms of braided…