On Nichols algebras of diagonal type

We give an explicit and essentially minimal list of defining relations of a Nichols algebra of diagonal type with finite root system. This list contains the well-known quantum Serre relations but also many new variations. A conjecture by Andruskiewitsch and Schneider states that any finite-dimension...

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Detalles Bibliográficos
Autor: Angiono, Iván Ezequiel
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2013
País:Argentina
Institución:Consejo Nacional de Investigaciones Científicas y Técnicas
Repositorio:CONICET Digital (CONICET)
Idioma:inglés
OAI Identifier:oai:ri.conicet.gov.ar:11336/11345
Acceso en línea:http://hdl.handle.net/11336/11345
Access Level:acceso abierto
Palabra clave:Hopf Algebras
Nichols Algebras
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
Descripción
Sumario:We give an explicit and essentially minimal list of defining relations of a Nichols algebra of diagonal type with finite root system. This list contains the well-known quantum Serre relations but also many new variations. A conjecture by Andruskiewitsch and Schneider states that any finite-dimensional pointed Hopf algebra over an algebraically closed field of characteristic zero is generated as an algebra by its group-like and skew-primitive elements. As an application of our main result, we prove the conjecture when the group of group-like elements is abelian.