Nichols algebras with many cubic relations

Nichols algebras of group type with many cubic relations are classified under a technical assumption on the structure of Hurwitz orbits of the third power of the underlying indecomposable rack. All such Nichols algebras are finite-dimensional, and their Hilbert series have a factorization into quant...

Descripción completa

Detalles Bibliográficos
Autores: Heckenberger, I., Lochmann, A., Vendramin, Claudio Leandro
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2015
País:Argentina
Institución:Consejo Nacional de Investigaciones Científicas y Técnicas
Repositorio:CONICET Digital (CONICET)
Idioma:inglés
OAI Identifier:oai:ri.conicet.gov.ar:11336/59632
Acceso en línea:http://hdl.handle.net/11336/59632
Access Level:acceso abierto
Palabra clave:Nichols algebras
Hurwitz orbits
Braid group
Cellular automata
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
Descripción
Sumario:Nichols algebras of group type with many cubic relations are classified under a technical assumption on the structure of Hurwitz orbits of the third power of the underlying indecomposable rack. All such Nichols algebras are finite-dimensional, and their Hilbert series have a factorization into quantum integers. Also, all known finite-dimensional elementary Nichols algebras turn out to have many cubic relations. The technical assumption of our theorem can be removed if a conjecture in the theory of cellular automata can be proven.