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
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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
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Palabras clave: | 3-transposition group; Hopf algebra; Hurwitz action; Nichols algebra; Rack |
Año: | 2012
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Volumen: | 17
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Número: | 1
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Página de inicio: | 157
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Página de fin: | 194
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DOI: |
http://dx.doi.org/10.1007/s00031-012-9176-7 |
Título revista: | Transformation Groups
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Título revista abreviado: | Transform. Groups
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ISSN: | 10834362
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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