On pointed Hopf algebras associated with alternating and dihedral groups

Details On pointed Hopf algebras associated with alternating and dihedral groups On pointed Hopf algebras associated with alternating and dihedral groups

2007-02-19

arxiv.org/abs/math/0702559v3

Rev. Uni\'on Mat. Argent.. 48-3, (2007), pp. 57-71

Mathematics

Quantum Algebra

v2: minor corrections, we remove Table 1 and change Remark 3.4; v3: minor corrections, we modify reference [FGV]; final versio

Scientific paper

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.

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