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...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2012 |
| País: | Argentina |
| Institución: | Consejo Nacional de Investigaciones Científicas y Técnicas |
| Repositorio: | CONICET Digital (CONICET) |
| Idioma: | inglés |
| OAI Identifier: | oai:ri.conicet.gov.ar:11336/217391 |
| Acceso en línea: | http://hdl.handle.net/11336/217391 |
| Access Level: | acceso abierto |
| Palabra clave: | 3-TRANSPOSITION GROUP HOPF ALGEBRA HURWITZ ACTION NICHOLS ALGEBRA RACK https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 |
| Sumario: | 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. |
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