Finite-dimensional pointed Hopf algebras over $\mathbb{S}_4$

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 $\mathbb{S}_4$ . We also describe all pointed Hopf algebras over $\mathbb{S}_5$ whose infinitesimal braiding is associated to the rack of transpositions.