On pointed Hopf algebras associated with alternating and dihedral groups

Abstract

We classify finite-dimensional complex pointed Hopf algebra with group of group-like elements isomorphic to A_5. We show that any pointed Hopf algebra with infinitesimal braiding associated with the conjugacy class of $\pi$ \in $A_n$ is infinite-dimensional if the order of $\pi$ is odd except for $\pi=(1 2 3)$ in $A_4$. We also study pointed Hopf algebras over the dihedral groups.