Dynamical quantum groups at roots of 1

TL;DR

This paper extends the theory of dynamical quantum groups to roots of unity, constructing dual weak Hopf algebras that exhibit self-duality, a novel property not seen in traditional quantum groups.

Contribution

It introduces a new class of self-dual dynamical quantum groups at roots of unity, generalizing existing theories and employing methods of Xu and Etingof-Varchenko.

Findings

Constructed dual weak Hopf algebras from dynamical twists

Demonstrated self-duality of these quantum groups at roots of unity

Extended the framework of dynamical quantum groups to roots of unity

Abstract

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.