A class of quantum doubles which are ribbon algebras

TL;DR

This paper explores a specific class of quantum doubles derived from pointed Hopf algebras with abelian coradicals, demonstrating that these doubles can form ribbon Hopf algebras, which are important in quantum topology.

Contribution

It identifies a new class of quantum doubles that are ribbon Hopf algebras, expanding the understanding of their structure and classification.

Findings

Quantum doubles of certain pointed Hopf algebras are ribbon Hopf algebras.

The classification builds on Andruskiewitsch and Schneider's work.

Provides new examples of ribbon Hopf algebras.

Abstract

Andruskiewitsch and Schneider classify a large class of pointed Hopf algebras with abelian coradical. The quantum double of each such Hopf algebra is investigated. The quantum doubles of a family of Hopf algebras from the above classification are ribbon Hopf algebras.