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…
On set-theoretical solutions of the quantum Yang-Baxter equation
- P. Etingof, T. Schedler, A. Soloviev
- Mathematics
- 22 July 1997
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…
Quantization of Lie bialgebras, II
- P. Etingof, D. Kazhdan
- Mathematics
- 1 September 1996
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…
Finite tensor categories
- P. Etingof, V. Ostrik
- Mathematics
- 4 January 2003
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…
Lectures on Quantum Groups
- P. Etingof, O. Schiffmann
- Mathematics
- 2001
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,…
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…
Parabolic induction and restriction functors for rational Cherednik algebras
- R. Bezrukavnikov, P. Etingof
- Mathematics
- 25 March 2008
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…
WEAKLY GROUP-THEORETICAL AND SOLVABLE FUSION CATEGORIES
- P. Etingof, D. Nikshych, V. Ostrik
- Mathematics
- 17 September 2008
Noncommutative geometry and quiver algebras
- W. Crawley-Boevey, P. Etingof, V. Ginzburg
- Mathematics
- 15 February 2005
Quantization of Lie bialgebras, I
- P. Etingof, D. Kazhdan
- Mathematics
- 6 June 1995
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…
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