Duke Mathematical Journal

Dynamical quantum groups at roots of 1

Pavel Etingof and Dmitri Nikshych

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Abstract

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

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

Dates
First available in Project Euclid: 5 August 2004

Permanent link to this document
https://projecteuclid.org/euclid.dmj/1091737126

Digital Object Identifier
doi:10.1215/S0012-7094-01-10814-4

Mathematical Reviews number (MathSciNet)
MR1831822

Zentralblatt MATH identifier
1023.17007

Subjects
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]

Citation

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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