A classification of Nichols algebras of semisimple Yetter-Drinfeld modules over non-abelian groups
Over fields of arbitrary characteristic we classify all braid-indecomposable tuples of at least two absolutely simple Yetter-Drinfeld modules over non-abelian groups such that the group is generated by the support of the tuple and the Nichols algebra of the tuple is finite-dimensional. Such tuples a...
| Autores: | , |
|---|---|
| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2017 |
| País: | Argentina |
| Institución: | Consejo Nacional de Investigaciones Científicas y Técnicas |
| Repositorio: | CONICET Digital (CONICET) |
| Idioma: | inglés |
| OAI Identifier: | oai:ri.conicet.gov.ar:11336/55447 |
| Acceso en línea: | http://hdl.handle.net/11336/55447 |
| Access Level: | acceso abierto |
| Palabra clave: | Hopf Algebra Nichols Algebra Weyl Groupoid https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 |
| Sumario: | Over fields of arbitrary characteristic we classify all braid-indecomposable tuples of at least two absolutely simple Yetter-Drinfeld modules over non-abelian groups such that the group is generated by the support of the tuple and the Nichols algebra of the tuple is finite-dimensional. Such tuples are classified in terms of analogs of Dynkin diagrams which encode much information about the Yetter-Drinfeld modules. We also compute the dimensions of these finite-dimensional Nichols algebras. Our proof uses essentially theWeyl groupoid of a tuple of simple Yetter-Drinfeld modules and our previous result on pairs. |
|---|