Families of finite-dimensional Hopf algebras with the Chevalley property

TL;DR

This paper introduces new families of finite-dimensional Hopf algebras with the Chevalley property, expanding the known examples by constructing twistings of quantum linear spaces that are neither pointed nor semisimple.

Contribution

It presents novel families of Hopf algebras with the Chevalley property, generalizing previous examples through twistings of quantum linear spaces.

Findings

New families of Hopf algebras with the Chevalley property are constructed.

These Hopf algebras are neither pointed nor semisimple.

The work extends known classifications by providing explicit examples.

Abstract

We introduce and study new families of finite-dimensional Hopf algebras with the Chevalley property that are not pointed nor semisimple arising as twistings of quantum linear spaces. These Hopf algebras generalize the examples introduced in [AEG], [EG1], [EG2].