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
π
\in
A
n
is infinite-dimensional if the order of
π
is odd except for
π=(123)
in
A
4
. We also study pointed Hopf algebras over the dihedral groups.