On the structure of (co-Frobenius) Hopf algebras

Autores
Andruskiewitsch, Nicolas; Cuadra, Juan
Año de publicación
2013
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
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).
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
Fil: Cuadra, Juan. Universidad de Almería; España
Materia
HOPF ALGEBRAS
QUANTUM GROUPS
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/2272
Acceder
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network_name_str CONICET Digital (CONICET)
spelling On the structure of (co-Frobenius) Hopf algebrasAndruskiewitsch, NicolasCuadra, JuanHOPF ALGEBRASQUANTUM GROUPShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We 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).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; ArgentinaFil: Cuadra, Juan. Universidad de Almería; EspañaEuropean Mathematical Society2013-03info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/2272Andruskiewitsch, Nicolas; Cuadra, Juan; On the structure of (co-Frobenius) Hopf algebras; European Mathematical Society; Journal of Noncommutative Geometry; 7; 1; 3-2013; 83-1041661-6952enginfo:eu-repo/semantics/altIdentifier/url/http://www.ems-ph.org/journals/show_abstract.php?issn=1661-6952&vol=7&iss=1&rank=2info:eu-repo/semantics/altIdentifier/url/http://arxiv.org/abs/1011.3457info:eu-repo/semantics/altIdentifier/doi/DOI:10.4171/JNCG/109info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T09:55:06Zoai:ri.conicet.gov.ar:11336/2272instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-03 09:55:06.514CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv On the structure of (co-Frobenius) Hopf algebras
title On the structure of (co-Frobenius) Hopf algebras
spellingShingle On the structure of (co-Frobenius) Hopf algebras
Andruskiewitsch, Nicolas
HOPF ALGEBRAS
QUANTUM GROUPS
title_short On the structure of (co-Frobenius) Hopf algebras
title_full On the structure of (co-Frobenius) Hopf algebras
title_fullStr On the structure of (co-Frobenius) Hopf algebras
title_full_unstemmed On the structure of (co-Frobenius) Hopf algebras
title_sort On the structure of (co-Frobenius) Hopf algebras
dc.creator.none.fl_str_mv Andruskiewitsch, Nicolas
Cuadra, Juan
author Andruskiewitsch, Nicolas
author_facet Andruskiewitsch, Nicolas
Cuadra, Juan
author_role author
author2 Cuadra, Juan
author2_role author
dc.subject.none.fl_str_mv HOPF ALGEBRAS
QUANTUM GROUPS
topic HOPF ALGEBRAS
QUANTUM GROUPS
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv 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).
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
Fil: Cuadra, Juan. Universidad de Almería; España
description 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).
publishDate 2013
dc.date.none.fl_str_mv 2013-03
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/2272
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
1661-6952
url http://hdl.handle.net/11336/2272
identifier_str_mv 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
1661-6952
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/http://www.ems-ph.org/journals/show_abstract.php?issn=1661-6952&vol=7&iss=1&rank=2
info:eu-repo/semantics/altIdentifier/url/http://arxiv.org/abs/1011.3457
info:eu-repo/semantics/altIdentifier/doi/DOI:10.4171/JNCG/109
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv European Mathematical Society
publisher.none.fl_str_mv European Mathematical Society
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 13.13397

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