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17 papers · 1 filter
The small quantum group as a quantum double
Pavel Etingof, Shlomo Gelaki
We prove that the quantum double of the quasi-Hopf algebra A_q(g) of dimension n^{dim g} attached in arXiv:math/0403096 to a simple complex Lie algebra g and a primitive root of un…
Weakly group-theoretical and solvable fusion categories
Pavel Etingof, Dmitri Nikshych, Victor Ostrik
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…
Quasisymmetric and unipotent tensor categories
Pavel Etingof, Shlomo Gelaki
We classify braided tensor categories over C of exponential growth which are quasisymmetric, i.e., the squared braiding is the identity on the product of any two simple objects. Th…
Monodromy of trigonometric KZ equations
Pavel Etingof, Nathan Geer
The famous Drinfeld-Kohno theorem for simple Lie algebras states that the monodromy representation of the Knizhnik-Zamolodchikov equations for these Lie algebras expresses explicit…
On Deformations of Associative Algebras
Roman Bezrukavnikov, Victor Ginzburg
In a classic paper, Gerstenhaber showed that first order deformations of an associative k-algebra A are controlled by the second Hochschild cohomology group of A. More generally, a…
Continuous Hecke algebras
Pavel Etingof, Wee Liang Gan, Victor Ginzburg
We study a generalization of graded Hecke algebras introduced by Drinfeld in 1986, in which the role of a finite group G is played by a reductive algebraic group. This includes con…