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Abstract:

We classify Nichols algebras of irreducible Yetter-Drinfeld modules over groups such that the underlying rack is braided and the homogeneous component of degree three of the Nichols algebra satisfies a given inequality. This assumption turns out to be equivalent to a factorization assumption on the Hilbert series. Besides the known Nichols algebras we obtain a new example. Our method is based on a combinatorial invariant of the Hurwitz orbits with respect to the action of the braid group on three strands. © 2012 Springer Science+Business Media, LLC.

Registro:

Documento: Artículo
Título:Braided racks, Hurwitz actions and Nichols algebras with many cubic relations
Autor:Heckenberger, I.; Lochmann, A.; Vendramin, L.
Filiación:Philipps-Universität Marburg, FB Mathematik und Informatik, Hans-Meerwein-Straße, 35032 Marburg, Germany
Depto. de Matemática, FCEyN, Universidad de Buenos Aires, Pab. 1, Ciudad Universitaria (1428), Buenos Aires, Argentina
Palabras clave:3-transposition group; Hopf algebra; Hurwitz action; Nichols algebra; Rack
Año:2012
Volumen:17
Número:1
Página de inicio:157
Página de fin:194
DOI: http://dx.doi.org/10.1007/s00031-012-9176-7
Título revista:Transformation Groups
Título revista abreviado:Transform. Groups
ISSN:10834362
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_10834362_v17_n1_p157_Heckenberger

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Citas:

---------- APA ----------
Heckenberger, I., Lochmann, A. & Vendramin, L. (2012) . Braided racks, Hurwitz actions and Nichols algebras with many cubic relations. Transformation Groups, 17(1), 157-194.
http://dx.doi.org/10.1007/s00031-012-9176-7
---------- CHICAGO ----------
Heckenberger, I., Lochmann, A., Vendramin, L. "Braided racks, Hurwitz actions and Nichols algebras with many cubic relations" . Transformation Groups 17, no. 1 (2012) : 157-194.
http://dx.doi.org/10.1007/s00031-012-9176-7
---------- MLA ----------
Heckenberger, I., Lochmann, A., Vendramin, L. "Braided racks, Hurwitz actions and Nichols algebras with many cubic relations" . Transformation Groups, vol. 17, no. 1, 2012, pp. 157-194.
http://dx.doi.org/10.1007/s00031-012-9176-7
---------- VANCOUVER ----------
Heckenberger, I., Lochmann, A., Vendramin, L. Braided racks, Hurwitz actions and Nichols algebras with many cubic relations. Transform. Groups. 2012;17(1):157-194.
http://dx.doi.org/10.1007/s00031-012-9176-7