Artículo
On the structure of (co-Frobenius) Hopf algebras
Fecha de publicación:
03/2013
Editorial:
European Mathematical Society
Revista:
Journal of Noncommutative Geometry
ISSN:
1661-6952
Idioma:
Inglés
Tipo de recurso:
Artículo publicado
Clasificación temática:
Resumen
We introduce a new filtration on Hopf algebras, the standard filtration, generalizing the coradical filtration. Its zeroth term, called the Hopf coradical, is the subalgebra generated by the coradical. We give a structure theorem: any Hopf algebra with injective antipode is a deformation of the bosonization of the Hopf coradical by its diagram, a connected graded Hopf algebra in the category of Yetter-Drinfeld modules over the latter. We discuss the steps needed to classify Hopf algebras in suitable classes accordingly. For the class of co-Frobenius Hopf algebras, we prove that a Hopf algebra is co-Frobenius if and only if its Hopf coradical is so and the diagram is finite dimensional. We also prove that the standard filtration of such Hopf algebras is finite. Finally, we show that extensions of co-Frobenius (resp. cosemisimple) Hopf algebras are co-Frobenius (resp. cosemisimple).
Palabras clave:
HOPF ALGEBRAS
,
QUANTUM GROUPS
Archivos asociados
Licencia
Identificadores
Colecciones
Articulos(CCT - CORDOBA)
Articulos de CTRO.CIENTIFICO TECNOL.CONICET - CORDOBA
Articulos de CTRO.CIENTIFICO TECNOL.CONICET - CORDOBA
Articulos(CIEM)
Articulos de CENT.INV.Y ESTUDIOS DE MATEMATICA DE CORDOBA(P)
Articulos de CENT.INV.Y ESTUDIOS DE MATEMATICA DE CORDOBA(P)
Citación
Andruskiewitsch, Nicolas; Cuadra, Juan; On the structure of (co-Frobenius) Hopf algebras; European Mathematical Society; Journal of Noncommutative Geometry; 7; 1; 3-2013; 83-104
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