Examples of finite-dimensional Hopf algebras with the dual Chevalley property

TL;DR

This paper constructs new finite-dimensional Hopf algebras with the dual Chevalley property by classifying semisimple Hopf algebras Morita-equivalent to group algebras over specific finite groups with non-trivial Nichols algebras.

Contribution

It provides a classification of certain semisimple Hopf algebras related to finite groups and Nichols algebras, expanding the known examples with the dual Chevalley property.

Findings

Identified all semisimple Hopf algebras Morita-equivalent to group algebras for selected groups.

Constructed new examples of Hopf algebras with the dual Chevalley property.

Linked Nichols algebra structures to the classification of Hopf algebras.

Abstract

We present new Hopf algebras with the dual Chevalley property by determining all semisimple Hopf algebras Morita-equivalent to a group algebra over a finite group, for a list of groups supporting a non-trivial finite-dimensional Nichols algebra.