Classification of finite-dimensional Hopf algebras over dual Radford algebras

TL;DR

This paper classifies all finite-dimensional Hopf algebras over an algebraically closed field of characteristic zero with specific coradicals, revealing new examples without the dual Chevalley property.

Contribution

It provides a complete classification of such Hopf algebras over dual Radford algebras of dimension 4p, introducing new examples lacking the dual Chevalley property.

Findings

Complete classification of Hopf algebras over dual Radford algebras

Discovery of new Hopf algebra families without dual Chevalley property

Extension of known classifications to prime dimensions p > 5

Abstract

We determine and classify all finite-dimensional Hopf algebras over an algebraically closed field of characteristic zero whose Hopf coradicals are isomorphic to dual Radford algebras of dimension $4p$ for a prime $p>5$. In particular, we obtain families of new examples of finite-dimensional Hopf algebras without the dual Chevalley property.