Author pages are created from data sourced from our academic publisher partnerships and public sources.

Publications Influence

Share This Author

On fusion categories

- P. Etingof, D. Nikshych, V. Ostrik
- Mathematics
- 7 March 2002

Using a variety of methods developed in the literature (in particular, the theory of weak Hopf algebras), we prove a number of general results about fusion categories in characteristic zero. We show… Expand

Fusion categories and homotopy theory

- P. Etingof, D. Nikshych, V. Ostrik, with an appendix by Ehud Meir
- Mathematics
- 17 September 2009

We apply the yoga of classical homotopy theory to classification problems of G-extensions of fusion and braided fusion categories, where G is a finite group. Namely, we reduce such problems to… Expand

WEAKLY GROUP-THEORETICAL AND SOLVABLE FUSION CATEGORIES

- P. Etingof, D. Nikshych, V. Ostrik
- Mathematics
- 17 September 2008

We introduce two new classes of fusion categories which are obtained by a certain procedure from finite groups – weakly group-theoretical categories and solvable categories. These are fusion… Expand

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

A Duality Theorem for Quantum Groupoids

- D. Nikshych
- Mathematics
- 29 December 1999

We prove a duality theorem for quantum groupoid (weak Hopf algebra) actions that extends the well-known result for usual Hopf algebras obtained in (BM) and (vdB).

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

The Witt group of non-degenerate braided fusion categories

- A. Davydov, Michael Mueger, D. Nikshych, V. Ostrik
- Mathematics, Physics
- 10 September 2010

Abstract We give a characterization of Drinfeld centers of fusion categories as non-degenerate braided fusion categories containing a Lagrangian algebra. Further we study the quotient of the monoid… Expand

An analogue of Radford's S4 formula for finite tensor categories

- P. Etingof, D. Nikshych, V. Ostrik
- Mathematics
- 27 April 2004

We develop the theory of Hopf bimodules for a finite rigid tensor category C. Then we use this theory to define a distinguished invertible object D of C and an isomorphism of tensor functors… Expand

Finite Quantum Groupoids and Their Applications

- D. Nikshych, L. Vainerman
- Mathematics
- 7 June 2000

We give a survey of the theory of finite quantum groupoids (weak Hopf algebras), including foundations of the theory and applications to finite depth subfactors, dynamical deformations of quantum… Expand

Invariants of knots and 3-manifolds from quantum groupoids

- D. Nikshych, V. Turaev, L. Vainerman
- Mathematics
- 10 June 2000

Abstract We use the categories of representations of finite-dimensional quantum groupoids (weak Hopf algebras) to construct ribbon and modular categories that give rise to invariants of knots and… Expand

...

1

2

3

4

5

...