Finite-dimensional pointed Hopf algebras with alternating groups are trivial
It is shown that Nichols algebras over alternating groups Am (m ≥ 5) are infinite dimensional. This proves that any complex finite dimensional pointed Hopf algebra with group of group-likes isomorphic to Am is isomorphic to the group algebra. In a similar fashion, it is shown that the Nichols algebr...
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| Autores principales: | , , , |
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| Formato: | JOUR |
| Materias: | |
| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_03733114_v190_n2_p225_Andruskiewitsch |
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| Sumario: | It is shown that Nichols algebras over alternating groups Am (m ≥ 5) are infinite dimensional. This proves that any complex finite dimensional pointed Hopf algebra with group of group-likes isomorphic to Am is isomorphic to the group algebra. In a similar fashion, it is shown that the Nichols algebras over the symmetric groups Sm are all infinite-dimensional, except maybe those related to the transpositions considered in Fomin and Kirillov (Progr Math 172:146-182, 1999), and the class of type (2, 3) in S5. 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 B(X, q) is infinite dimensional, q an arbitrary cocycle. © 2010 Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag. |
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