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To any finite group Γ ⊂ Sp(V) of automorphisms of a symplectic vector space V we associate a new multi-parameter deformation, Hκ, of the algebra C[V ]#Γ, smash product of Γ with the polynomial… (More)

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… (More)

Recently V.Drinfeld formulated a number of problems in quantum group theory. In particular, he suggested to consider ``set-theoretical'' solutions of the quantum Yang-Baxter equation, i.e. solutions… (More)

The classical Yang-Baxter equation (CYBE) is an algebraic equation central in the theory of integrable systems. Its solutions were classified by Belavin and Drinfeld. Quantization of CYBE led to the… (More)

The quantum dynamical Yang-Baxter (QDYB) equation is a useful generalization of the quantum Yang-Baxter (QYB) equation. This generalization was introduced by Gervais, Neveu, and Felder. Unlike the… (More)

We start the general structure theory of not necessarily semisimple finite tensor categories, generalizing the results in the semisimple case (i. e. for fusion categories), obtained recently in our… (More)

The goal of this paper is to introduce and study two classes of fusion categories (over C): weakly group-theoretical categories and solvable categories. Namely, recall ([GNk]) that a fusion category… (More)

Let G be a simple simply connected algebraic group over C with Lie algebra g. Given a parabolic subgroup P ⊂ G, in [1] the first author introduced a certain generating function Z aff G,P. Roughly… (More)

Parabolic induction and restriction functors play an important role in the representation theory of finite and affine Hecke algebras. This makes it desirable to generalize them to the setting of… (More)