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 $\pi =(123)$ in $A_4$. We also study pointed Hopf algebras over the dihedral groups.

v2: minor corrections, we remove Table 1 and change Remark 3.4; v3: minor corrections, we modify reference [FGV]; final version to appear in Rev. Unión Mat. Argent., 17 pages

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