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dc.contributor.author
Andruskiewitsch, Nicolas
dc.contributor.author
Cuadra, Juan
dc.date.available
2015-10-01T19:04:57Z
dc.date.issued
2013-03
dc.identifier.citation
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
dc.identifier.issn
1661-6952
dc.identifier.uri
http://hdl.handle.net/11336/2272
dc.description.abstract
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).
dc.format
application/pdf
dc.language.iso
eng
dc.publisher
European Mathematical Society
dc.rights
info:eu-repo/semantics/openAccess
dc.rights.uri
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.subject
HOPF ALGEBRAS
dc.subject
QUANTUM GROUPS
dc.subject.classification
Matemática Pura
dc.subject.classification
Matemáticas
dc.subject.classification
CIENCIAS NATURALES Y EXACTAS
dc.title
On the structure of (co-Frobenius) Hopf algebras
dc.type
info:eu-repo/semantics/article
dc.type
info:ar-repo/semantics/artículo
dc.type
info:eu-repo/semantics/publishedVersion
dc.date.updated
2016-03-30 10:35:44.97925-03
dc.journal.volume
7
dc.journal.number
1
dc.journal.pagination
83-104
dc.journal.pais
Suiza
dc.journal.ciudad
Zürich
dc.description.fil
Fil: Andruskiewitsch, Nicolas. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Córdoba. Centro de Investigación y Estudios de Matemática de Córdoba(p); Argentina. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina
dc.description.fil
Fil: Cuadra, Juan. Universidad de Almería; España
dc.journal.title
Journal of Noncommutative Geometry
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/url/http://www.ems-ph.org/journals/show_abstract.php?issn=1661-6952&vol=7&iss=1&rank=2
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/url/http://arxiv.org/abs/1011.3457
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/doi/http://dx.doi.org/DOI:10.4171/JNCG/109
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