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Quantization of Lie bialgebras, II
Abstract. This paper is a continuation of [EK]. We show that the quantization procedure of [EK] is given by universal acyclic formulas and defines a functor from the category of Lie bialgebras to the
On fusion categories
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
On set-theoretical solutions of the quantum Yang-Baxter equation
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
Finite tensor categories
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
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 to
Lectures on Quantum Groups
Revised second edition. The text covers the material presented for a graduate-level course on quantum groups at Harvard University. Covered topics include: Poisson algebras and quantization,
Parabolic induction and restriction functors for rational Cherednik algebras
Abstract.We introduce parabolic induction and restriction functors for rational Cherednik algebras, and study their basic properties. Then we discuss applications of these functors to representation
Quantization of Lie bialgebras, I
In the paper [Dr3] V. Drinfeld formulated a number of problems in quantum group theory. In particular, he raised the question about the existence of a quantization for Lie bialgebras, which arose
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
Noncommutative geometry and quiver algebras
Abstract We develop a new framework for noncommutative differential geometry based on double derivations. This leads to the notion of moment map and of Hamiltonian reduction in noncommutative