Braided racks, Hurwitz actions and Nichols algebras with many cubic relations
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...
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| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_10834362_v17_n1_p157_Heckenberger |
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todo:paper_10834362_v17_n1_p157_Heckenberger2023-10-03T16:04:03Z Braided racks, Hurwitz actions and Nichols algebras with many cubic relations Heckenberger, I. Lochmann, A. Vendramin, L. 3-transposition group Hopf algebra Hurwitz action Nichols algebra Rack 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. Fil:Vendramin, L. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_10834362_v17_n1_p157_Heckenberger |
| institution |
Universidad de Buenos Aires |
| institution_str |
I-28 |
| repository_str |
R-134 |
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| topic |
3-transposition group Hopf algebra Hurwitz action Nichols algebra Rack |
| spellingShingle |
3-transposition group Hopf algebra Hurwitz action Nichols algebra Rack Heckenberger, I. Lochmann, A. Vendramin, L. Braided racks, Hurwitz actions and Nichols algebras with many cubic relations |
| topic_facet |
3-transposition group Hopf algebra Hurwitz action Nichols algebra Rack |
| description |
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. |
| format |
JOUR |
| author |
Heckenberger, I. Lochmann, A. Vendramin, L. |
| author_facet |
Heckenberger, I. Lochmann, A. Vendramin, L. |
| author_sort |
Heckenberger, I. |
| title |
Braided racks, Hurwitz actions and Nichols algebras with many cubic relations |
| title_short |
Braided racks, Hurwitz actions and Nichols algebras with many cubic relations |
| title_full |
Braided racks, Hurwitz actions and Nichols algebras with many cubic relations |
| title_fullStr |
Braided racks, Hurwitz actions and Nichols algebras with many cubic relations |
| title_full_unstemmed |
Braided racks, Hurwitz actions and Nichols algebras with many cubic relations |
| title_sort |
braided racks, hurwitz actions and nichols algebras with many cubic relations |
| url |
http://hdl.handle.net/20.500.12110/paper_10834362_v17_n1_p157_Heckenberger |
| work_keys_str_mv |
AT heckenbergeri braidedrackshurwitzactionsandnicholsalgebraswithmanycubicrelations AT lochmanna braidedrackshurwitzactionsandnicholsalgebraswithmanycubicrelations AT vendraminl braidedrackshurwitzactionsandnicholsalgebraswithmanycubicrelations |
| _version_ |
1782030047672008704 |