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On braided fusion categories I
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 give a comprehensive andExpand
Nilpotent fusion categories
Abstract 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 fusionExpand
On the exponent of finite-dimensional Hopf algebras
One of the classical notions of group theory is the notion of the exponent of a group. The exponent of a group is the least common multiple of orders of its elements. In this paper we generalize theExpand
Triangular Hopf algebras with the Chevalley property
We say that a Hopf algebra has the Chevalley property if the tensor product of any two simple modules over this Hopf algebra is semisimple. In this paper we classify finite dimensional triangularExpand
Basic quasi-Hopf algebras of dimension
Abstract We construct new finite dimensional basic quasi-Hopf algebras A ( q ) of dimension n 3 , n > 2 , parametrized by primitive roots of unity q of order n 2 , with radical of codimension n ,Expand
Isocategorical groups
It is well known that if two finite groups have the same symmetric tensor categories of representations over C, then they are isomorphic. We study the following question: when do two finite groupsExpand
Some properties of finite-dimensional semisimple Hopf algebras
Kaplansky conjectured that if H is a finite-dimensional semisimple Hopf algebra over an algebraically closed field k of characteristic 0, then H is of Frobenius type (i.e. if V is an irreducibleExpand
On Finite-Dimensional Semisimple and Cosemisimple Hopf Algebras in Positive Characteristic
Recently, important progress has been made in the study of finite-dimensional semisimple Hopf algebras over a field of characteristic zero. Yet, very little is known over a field of positiveExpand
On radically graded finite dimensional quasi-Hopf algebras
Let p be a prime, and denote the class of radically graded finite dimensional quasi-Hopf algebras over C, whose radical has codimension p, by RG(p). The purpose of this paper is to continue theExpand
We characterize a natural class of modular categories of prime power Frobenius-Perron dimension as representation categories of twisted dou- bles of finite p-groups. We also show that a nilpotentExpand