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Fusion categories and homotopy theory
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 toExpand
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 fusionExpand
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
The Witt group of non-degenerate braided fusion categories
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 monoidExpand
Module categories over the Drinfeld double of a finite group
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 isomorphismExpand
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 theExpand
Cohomology of Spaltenstein varieties
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 ofExpand
On formal codegrees of fusion categories
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.
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
Character D-modules via Drinfeld center of Harish-Chandra bimodules
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 convolutionExpand