Related papers: Generalized Tambara-Yamagami categories
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 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…
Tambara and Yamagami investigated a simple set of fusion rules with only one non-invertible object, and proved under which circumstances those rules could be given a coherent associator. We consider a generalization of such fusion rules to…
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.…
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 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…
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 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 determine the fusion rules of the equivariantization of a fusion category $\mathcal{C}$ under the action of a finite group $G$ in terms of the fusion rules of $\mathcal{C}$ and group-theoretical data associated to the group action. As an…
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…
``Fusion rules'' are laws of multiplication among eigenspaces of an idempotent. We establish fusion rules for flexible power-associative algebras, following Albert. We define the notion of an axis in the noncommutative setting (compare with…
We compute and classify the irreducible non-negative integer matrix (NIM-)representations of two proposed generalizations of the Tambara-Yamagami fusion ring, as studied by Jordan-Larson and Galindo-Lentner-M\"oller, respectively. We also…
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…
In this paper, we first show for a slightly degenerate pre-modular fusion category $\mathcal{C}$ that squares of dimensions of simple objects divide half of the dimension of $\mathcal{C}$, and that slightly degenerate fusion categories of…
We present a method to generate all fusion rings of a specific rank and multiplicity. This method was used to generate exhaustive lists of fusion rings up to order 9 for several multiplicities. We introduce a class of non-commutative fusion…
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 determine all reduced saturated fusion systems supported on a finite $p$-group of nilpotency class two. As a consequence, we obtain a new proof of Gilman & Gorenstein's classification of finite simple groups with class two Sylow…
In this paper we extend categorically the notion of a finite nilpotent group to fusion categories. To this end, we first analyze the trivial component of the universal grading of a fusion category C, and then introduce the upper central…
We classify all fusion categories for a given set of fusion rules with three simple object types. If a conjecture of Ostrik is true, our classification completes the classification of fusion categories with three simple object types. To…
We introduce a weakening of the notion of fusion 2-category given in arXiv:1812.11933. Then, we establish a number of properties of (multi)fusion 2-categories. Finally, we describe the fusion rule of the fusion 2-categories associated to…