Related papers: Structure, examples and classification for general…
In this paper, we study the structure of a generalized near-group fusion category and classified it when it is slightly degenerate.
A near-group category is an additively semisimple category with a product such that all but one of the simple objects is invertible. We classify braided structures on near-group categories, and give explicit numerical formulas for their…
This is a study of weakly integral braided fusion categories with elementary fusion rules to determine which possess nondegenerately braided extensions of theoretically minimal dimension, or equivalently in this case, which satisfy the…
We classify braided generalized near-group fusion categories whose global dimension is not an integer; there are exactly two up to Grothendieck equivalence and taking products with braided pointed fusion categories.
A near-group fusion category is a fusion category C where all but 1 simple objects are invertible. Examples of these include the Tambara-Yamagami categories and the even sectors of the E6 and affine-D5 subfactors, though there are…
We establish rank-finiteness for the class of $G$-crossed braided fusion categories, generalizing the recent result for modular categories and including the important case of braided fusion categories. This necessitates a study of slightly…
Fusion rules generalize groups by allowing multivalued multiplication. Groups are fusion rules of simple current index 1. We classify nilpotent (in the sense of Gelaki and Nikshych) fusion rules of simple current index 2, and characterize…
Noncommutative near-group fusion categories were completely classified in the previous work of the first named author by using an operator algebraic method (and hence under the assumption of unitarity), and they were shown to be group…
We establish some relations between the orders of simple objects in a fusion category and the structure of its universal grading group. We consider fusion categories which have a faithful simple object and show that its universal grading…
Let C be a fusion category which is an extension of a fusion category D by a finite group G. We classify module categories over C in terms of module categories over D and the extension data (c,M,a) of C. We also describe functor categories…
We introduce group-theoretical fusion 2-categories, a strong categorification of the notion of a group-theoretical fusion 1-category. Physically speaking, such fusion 2-categories arise by gauging subgroups of a global symmetry. We show…
We abstract the study of irreducible characters of finite groups vanishing on all but two conjugacy classes, initiated by S. Gagola, to irreducible characters of fusion rings whose kernel has maximal rank. These near-integral fusion rings…
We consider the possibility of semisimple tensor categories whose fusion rule includes exactly one noninvertible simple object. Conditions are given for the existence or nonexistence of coherent associative structures for such fusion rules,…
We advance the classification of fusion categories in two directions. Firstly, we completely classify integral fusion categories -- and consequently, semi-simple Hopf algebras -- of dimension $pq^2$, where $p$ and $q$ are distinct primes.…
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.
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…
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 consider notions of metrized categories, and then approximate categorical structures defined by a function of three variables generalizing the notion of $2$-metric space. We prove an embedding theorem giving sufficient conditions for an…
We introduce the notion of a matched pair of fusion rings and fusion categories, generalizing the one for groups. Using this concept, we define the bicrossed product of fusion rings and fusion categories and we construct exact…
We classify certain $\mathbb{Z}_2 $-graded extensions of generalized Haagerup categories in terms of numerical invariants satisfying polynomial equations. In particular, we construct a number of new examples of fusion categories, including:…