483 citations · 1.7k across the 181 of their papers we have counts for
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The Representation Theory of Co-triangular Semisimple Hopf Algebras
Pavel Etingof, Shlomo Gelaki
In a previous paper we prove that any semisimple triangular Hopf algebra A over an algebraically closed field of characteristic 0 (say the field of complex numbers C) is obtained f…
On the exponent of finite-dimensional Hopf algebras
Pavel Etingof, Shlomo Gelaki
One of the classical notions of group theory is the notion of the exponent of a group. The exponent of a group is the least common multiple of orders of its elements. In this paper…
Quantization of geometric classical r-matrices
Pavel Etingof, Alexandre Soloviev
In this note we define geometric classical r-matrices and quantum R-matrices, and show how any geometric classical r-matrix can be quantized to a geometric quantum R-matrix. This i…
On highest weight modules over elliptic quantum groups
Pavel Etingof, Olivier Schiffmann
The purpose of this note is to define and construct highest weight modules for Felder's elliptic quantum groups. This is done by using exchange matrices for intertwining operators…
Quantization of Lie bialgebras, V
Pavel Etingof, David Kazhdan
This paper is a continuation of "Quantization of Lie bialgebras I-IV". The goal of this paper is to define and study the notion of a quantum vertex operator algebra in the setting…
Quantum determinants and quasideterminants
Pavel Etingof, Vladimir Retakh
The notion of a quasideterminant and a quasiminor of a matrix A=(a_{ij}) with not necessarily commuting entries was introduced recently by I.Gelfand and the second author. The ordi…
A method of construction of finite-dimensional triangular semisimple Hopf algebras
Pavel Etingof, Shlomo Gelaki
The goal of this paper is to give a new method of constructing finite-dimensional semisimple triangular Hopf algebras, including minimal ones which are non-trivial (i.e. not group…
On Finite-Dimensional Semisimple and Cosemisimple Hopf Algebras in Positive Characteristic
Pavel Etingof, Shlomo Gelaki
Recently, important progress has been made in the study of finite-dimensional semisimple Hopf algebras over a field of characteristic zero. Yet, very little is known over a field o…
A link between two elliptic quantum groups
Pavel Etingof, Olivier Schiffmann
We construct a fully faithful functor from the category C_F of finite-dimensional representations of Felder's (dynamical) elliptic quantum group E_{tau,gamma}(gl(n)) to a cretain c…
Semisimple Hopf algebras of dimension pq are trivial
Pavel Etingof, Shlomo Gelaki
Masuoka proved that for a prime p, semisimple Hopf algebras of dimension 2p over an algebraically closed field k of characteristic 0, are trivial (i.e. are either group algebras or…
Set-theoretical solutions to the quantum Yang-Baxter equation
Pavel Etingof, Travis Schedler, Alexandre Soloviev
In 1992 VDrinfeld formulated a number of problems in quantum group theory. In particular, he suggested to consider ``set-theoretical'' solutions to the quantum Yang-Baxter equat…
Quantization of Lie bialgebras, IV
Pavel Etingof, David Kazhdan
This paper is a continuation of "Quantization of Lie bialgebras, III" (q-alg/9610030, revised version). In QLB-III, we introduced the Hopf algebra F(R)_\z associated to a quantum R…