Duke Mathematical Journal

Dynamical quantum groups at roots of 1

Pavel Etingof and Dmitri Nikshych

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Given a dynamical twist for a finite-dimensional Hopf algebra, we construct two weak Hopf algebras, using methods of P. Xu and of P. Etingof and A. Varchenko, and we show that they are dual to each other. We generalize the theory of dynamical quantum groups to the case when the quantum parameter q is a root of unity. These objects turn out to be self-dual—which is a fundamentally new property, not satisfied by the usual Drinfeld-Jimbo quantum groups.

Article information

Duke Math. J., Volume 108, Number 1 (2001), 135-168.

First available in Project Euclid: 5 August 2004

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 17B37: Quantum groups (quantized enveloping algebras) and related deformations [See also 16T20, 20G42, 81R50, 82B23]
Secondary: 81R50: Quantum groups and related algebraic methods [See also 16T20, 17B37]


Etingof, Pavel; Nikshych, Dmitri. Dynamical quantum groups at roots of 1. Duke Math. J. 108 (2001), no. 1, 135--168. doi:10.1215/S0012-7094-01-10814-4. https://projecteuclid.org/euclid.dmj/1091737126

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