Finite dimensional Hopf algebras over the dual group algebra of the symmetric group in three letters

TL;DR

This paper classifies finite-dimensional Hopf algebras with a specific coradical structure related to the symmetric group S_3 and introduces a new family of such algebras of dimension 72.

Contribution

It provides a classification of these Hopf algebras and constructs a novel infinite family of them of dimension 72.

Findings

Classification of Hopf algebras with coradical isomorphic to functions on S_3

Introduction of a new infinite family of Hopf algebras of dimension 72

Detailed structural description of these algebras

Abstract

We classify finite-dimensional Hopf algebras whose coradical is isomorphic to the algebra of functions on S_3. We describe a new infinite family of Hopf algebras of dimension 72.