%0 Journal Article
%T Finite-dimensional pointed Hopf algebras with alternating groups are trivial
%A N. Andruskiewitsch
%A F. Fantino
%A M. Gra£ża
%A L. Vendramin
%J Mathematics
%D 2008
%I arXiv
%R 10.1007/s10231-010-0147-0
%X It is shown that Nichols algebras over alternating groups A_m, m>4, are infinite dimensional. This proves that any complex finite dimensional pointed Hopf algebra with group of group-likes isomorphic to A_m is isomorphic to the group algebra. In a similar fashion, it is shown that the Nichols algebras over the symmetric groups S_m are all infinite-dimensional, except maybe those related to the transpositions considered in [FK], and the class of type (2,3) in S_5. We also show that any simple rack X arising from a symmetric group, with the exception of a small list, collapse, in the sense that the Nichols algebra of (X,q) is infinite dimensional, for q an arbitrary cocycle. arXiv:0904.3978 is included here.
%U http://arxiv.org/abs/0812.4628v7