Finite-dimensional Hopf algebras over the smallest non-pointed basic Hopf algebra

TL;DR

This paper classifies certain finite-dimensional Hopf algebras over an algebraically closed field of characteristic zero, revealing new Nichols algebras and Hopf algebras without the dual Chevalley property, under specific grading assumptions.

Contribution

It provides a classification of Hopf algebras with a specific coradical structure, introducing new Nichols algebras and examples of Hopf algebras lacking the dual Chevalley property.

Findings

New Nichols algebras of non-diagonal type identified

Classification of finite-dimensional Hopf algebras with given coradical

Examples of Hopf algebras without the dual Chevalley property

Abstract

We classify finite-dimensional Hopf algebras over an algebraically closed field of characteristic zero whose Hopf coradcial is isomorphic to the smallest non-pointed basic Hopf algebra, under the assumption that the diagrams are strictly graded. In particular, we obtain some new Nichols algebras of non-diagonal type and new finite-dimensional Hopf algebras without the dual Chevalley property.