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Abstract:

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.

Registro:

Documento: Artículo
Título:Finite-dimensional pointed Hopf algebras with alternating groups are trivial
Autor:Andruskiewitsch, N.; Fantino, F.; Graña, M.; Vendramin, L.
Filiación:Facultad de Matemática, Astronomía y Física, Universidad Nacional de Córdoba. CIEM, CONICET, Medina Allende s/n, Ciudad Universitaria, 5000 Córdoba, Argentina
Departamento de Matemática, FCEyN, Universidad de Buenos Aires, Pab. I, Ciudad Universitaria, 1428 Buenos Aires, Argentina
Instituto de Ciencias, Universidad de Gral. Sarmiento, J.M. Gutierrez 1150, Los Polvorines, 1653 Buenos Aires, Argentina
Palabras clave:Nichols algebras; Pointed Hopf algebras; Racks
Año:2011
Volumen:190
Número:2
Página de inicio:225
Página de fin:245
DOI: http://dx.doi.org/10.1007/s10231-010-0147-0
Título revista:Annali di Matematica Pura ed Applicata
Título revista abreviado:Ann. Mat. Pura Appl.
ISSN:03733114
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_03733114_v190_n2_p225_Andruskiewitsch

Referencias:

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Citas:

---------- APA ----------
Andruskiewitsch, N., Fantino, F., Graña, M. & Vendramin, L. (2011) . Finite-dimensional pointed Hopf algebras with alternating groups are trivial. Annali di Matematica Pura ed Applicata, 190(2), 225-245.
http://dx.doi.org/10.1007/s10231-010-0147-0
---------- CHICAGO ----------
Andruskiewitsch, N., Fantino, F., Graña, M., Vendramin, L. "Finite-dimensional pointed Hopf algebras with alternating groups are trivial" . Annali di Matematica Pura ed Applicata 190, no. 2 (2011) : 225-245.
http://dx.doi.org/10.1007/s10231-010-0147-0
---------- MLA ----------
Andruskiewitsch, N., Fantino, F., Graña, M., Vendramin, L. "Finite-dimensional pointed Hopf algebras with alternating groups are trivial" . Annali di Matematica Pura ed Applicata, vol. 190, no. 2, 2011, pp. 225-245.
http://dx.doi.org/10.1007/s10231-010-0147-0
---------- VANCOUVER ----------
Andruskiewitsch, N., Fantino, F., Graña, M., Vendramin, L. Finite-dimensional pointed Hopf algebras with alternating groups are trivial. Ann. Mat. Pura Appl. 2011;190(2):225-245.
http://dx.doi.org/10.1007/s10231-010-0147-0