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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

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

Module categories over the Drinfeld double of a finite group

- V. Ostrik
- Mathematics
- 14 February 2002

Let C be a (semisimple abelian) monoidal category. A module category over C is a (semisimple abelian) category M together with a functor C×M → M and an associativity constraint (= natural isomorphism… Expand

On blocks of Deligne's category Re _ p ( S t )

Recently P. Deligne introduced the tensor category Rep(S_t) (for t not necessarily an integer) which in a certain precise sense interpolates the categories Rep(S_d) of representations of the… Expand

Cohomology of Spaltenstein varieties

- J. Brundan, V. Ostrik
- Mathematics
- 15 December 2010

We give a presentation for the cohomology algebra of the Spaltenstein variety of all partial flags annihilated by a fixed nilpotent matrix, generalizing the description of the cohomology algebra of… Expand

On formal codegrees of fusion categories

- V. Ostrik
- Mathematics
- 17 October 2008

We prove a general result which implies that the global and Frobenius-Perron dimensions of a fusion category generate Galois invariant ideals in the ring of algebraic integers.

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

Character D-modules via Drinfeld center of Harish-Chandra bimodules

- R. Bezrukavnikov, M. Finkelberg, V. Ostrik
- Mathematics
- 9 February 2009

The category of character D-modules is realized as Drinfeld center of the abelian monoidal category of Harish-Chandra bimodules. Tensor product of Harish-Chandra bimodules is related to convolution… Expand

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