Finite dimensional pointed Hopf algebras over S_4

TL;DR

This paper classifies finite dimensional pointed Hopf algebras over the symmetric group S_4 and describes certain Hopf algebras over S_5 related to transpositions, advancing understanding of algebraic structures linked to these groups.

Contribution

It provides a complete classification of pointed Hopf algebras over S_4 and characterizes specific cases over S_5, extending previous algebraic classifications.

Findings

Classified all finite dimensional pointed Hopf algebras over S_4.

Described pointed Hopf algebras over S_5 with transposition-based infinitesimal braiding.

Enhanced understanding of algebraic structures associated with symmetric groups.

Abstract

Let k be an algebraically closed field of characteristic 0. We conclude the classification of finite dimensional pointed Hopf algebras whose group of group-likes is S_4. We also describe all pointed Hopf algebras over S_5 whose infinitesimal braiding is associated to the rack of transpositions.