On Hopf algebras over basic Hopf algebras of dimension 24

TL;DR

This paper classifies certain finite-dimensional Hopf algebras over algebraically closed fields of characteristic zero, focusing on those with a specific basic Hopf algebra of dimension 24 as the coradical and indecomposable infinitesimal braidings.

Contribution

It provides a classification of new finite-dimensional Hopf algebras with a given coradical structure, including examples without the dual Chevalley property.

Findings

Identification of families of new Hopf algebras

Construction of examples lacking the dual Chevalley property

Extension of classification results to non-pointed cases

Abstract

We determine finite-dimensional Hopf algebras over an algebraically closed field of characteristic zero, whose Hopf coradical is isomorphic to a non-pointed basic Hopf algebra of dimension $24$ and the infinitesimal braidings are indecomposable objects. In particular, we obtain families of new finite-dimensional Hopf algebras without the dual Chevalley property.