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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Detalles Bibliográficos
Autores: Heckenberger, I., Lochmann, A., Vendramin, Claudio Leandro
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
Descripción
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.