Finite-dimensional pointed Hopf algebras with alternating groups are trivial

Details Finite-dimensional pointed Hopf algebras with alternating groups are trivial Finite-dimensional pointed Hopf algebras with alternating groups are trivial

2008-12-25

arxiv.org/abs/0812.4628v7

Ann. Mat. Pura Appl. (4) 190 (2011), no. 2, 225-245

Mathematics

Quantum Algebra

Changes in version 7: We eliminate the Subsection 3.3 and references to type C throughout the paper. We remove Lemma 3.24, Pro

Scientific paper

10.1007/s10231-010-0147-0

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.

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