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On braided fusion categories I

- V. Drinfeld, S. Gelaki, D. Nikshych, V. Ostrik
- Mathematics
- 2 June 2009

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 and… Expand

Nilpotent fusion categories

- S. Gelaki, D. Nikshych
- Mathematics
- 24 October 2006

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 fusion… Expand

On the exponent of finite-dimensional Hopf algebras

- P. Etingof, S. Gelaki
- Mathematics
- 28 December 1998

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 the… Expand

Triangular Hopf algebras with the Chevalley property

- N. Andruskiewitsch, P. Etingof, S. Gelaki
- Mathematics
- 31 August 2000

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 triangular… Expand

Basic quasi-Hopf algebras of dimension

- S. Gelaki
- Mathematics
- 1 June 2005

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

- P. Etingof, S. Gelaki
- Mathematics
- 31 July 2000

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 groups… Expand

Some properties of finite-dimensional semisimple Hopf algebras

- P. Etingof, S. Gelaki
- Mathematics
- 11 December 1997

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 irreducible… Expand

On Finite-Dimensional Semisimple and Cosemisimple Hopf Algebras in Positive Characteristic

- P. Etingof, S. Gelaki
- Mathematics
- 22 May 1998

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 positive… Expand

On radically graded finite dimensional quasi-Hopf algebras

- P. Etingof, S. Gelaki
- Mathematics
- 4 March 2004

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 the… Expand

GROUP-THEORETICAL PROPERTIES OF NILPOTENT MODULAR CATEGORIES

- V. Drinfeld, S. Gelaki, D. Nikshych, V. Ostrik
- Mathematics
- 2 April 2007

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 nilpotent… Expand

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