Dynamical quantum groups at roots of 1

By Pavel Etingof, D. Nikshych. 2000

77 citations recorded by the source corpus.

Given a dynamical twist for a finite dimensional Hopf algebra we construct two weak Hopf algebras, using methods of Xu and Etingof-Varchenko, and 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.

Subfields: Algebra and Number Theory, Geometry and Topology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/47deacdfb46177c46c717981f66564a69754f7e3

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Citations in the corpus

Hopf Algebroids (2008, unknown): “Alternative notions 40 Acknowledgement 42 References 42”
On the Structure of Weak Hopf Algebras (2001, methodology): “This appears to be a natural property, since it is satisfied by dynamical quantum groups [4] and weak Hopf algebras arising as symmetries of Jones-von Neumann subfactors [13], [14].”
Bialgebroids, ×A-Bialgebras and Duality☆ (2002, unknown): “Q A ] 7 N ov 2 00 1”
On finite-dimensional Hopf algebras (2014, background): “Examples of 81 twistings not mentioned elsewhere in this report are in [31, 65].”
Weak Hopf algebras and quantum groupoids (2002, methodology): “Weak Hopf algebras were defined by Böhm and Szlachányi [2], see also the recent survey [15] by Nikshych and Văınerman and the literature cited there.”
Bialgebroid actions on depth two extensions and duality (2003, methodology): “4] since R 1⁄4 M: In case R is not semisimple, A is a bialgebroid over R which is not a weak bialgebra [11].”