Finite-dimensional pointed or copointed Hopf algebras over affine racks

Autores
Garcia Iglesias, Agustin; Vay, Cristian Damian
Año de publicación
2014
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We study the pointed or copointed liftings of Nichols algebras associated to affine racks and constant cocycles for any finite group admitting a principal YD-realization of these racks. In the copointed case we complete the classification for the six affine racks whose Nichols algebra is known to be of finite dimension. In the pointed case our method allows us to finish four of them. In all of the cases the Hopf algebras obtained turn out to be cocycle deformations of their associated graded Hopf algebras. All of them are new examples of finite-dimensional copointed or pointed Hopf algebras over non-abelian groups.
Fil: Garcia Iglesias, Agustin. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentina
Fil: Vay, Cristian Damian. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentina. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina
Materia
Pointed Hopf Algebras
Copointed Hopf Algebras
Affine Racks
Nichols Algebras
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:11336/31951
Acceder
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network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Finite-dimensional pointed or copointed Hopf algebras over affine racksGarcia Iglesias, AgustinVay, Cristian DamianPointed Hopf AlgebrasCopointed Hopf AlgebrasAffine RacksNichols Algebrashttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We study the pointed or copointed liftings of Nichols algebras associated to affine racks and constant cocycles for any finite group admitting a principal YD-realization of these racks. In the copointed case we complete the classification for the six affine racks whose Nichols algebra is known to be of finite dimension. In the pointed case our method allows us to finish four of them. In all of the cases the Hopf algebras obtained turn out to be cocycle deformations of their associated graded Hopf algebras. All of them are new examples of finite-dimensional copointed or pointed Hopf algebras over non-abelian groups.Fil: Garcia Iglesias, Agustin. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; ArgentinaFil: Vay, Cristian Damian. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentina. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; ArgentinaAcademic Press Inc Elsevier Science2014-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/31951Vay, Cristian Damian; Garcia Iglesias, Agustin; Finite-dimensional pointed or copointed Hopf algebras over affine racks; Academic Press Inc Elsevier Science; Journal Of Algebra; 397; 1-2014; 379-4060021-8693CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1016/j.jalgebra.2013.09.009info:eu-repo/semantics/altIdentifier/url/http://www.sciencedirect.com/science/article/pii/S0021869313004985info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T10:27:59Zoai:ri.conicet.gov.ar:11336/31951instacron: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:34982025-09-29 10:27:59.591CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Finite-dimensional pointed or copointed Hopf algebras over affine racks
title Finite-dimensional pointed or copointed Hopf algebras over affine racks
spellingShingle Finite-dimensional pointed or copointed Hopf algebras over affine racks
Garcia Iglesias, Agustin
Pointed Hopf Algebras
Copointed Hopf Algebras
Affine Racks
Nichols Algebras
title_short Finite-dimensional pointed or copointed Hopf algebras over affine racks
title_full Finite-dimensional pointed or copointed Hopf algebras over affine racks
title_fullStr Finite-dimensional pointed or copointed Hopf algebras over affine racks
title_full_unstemmed Finite-dimensional pointed or copointed Hopf algebras over affine racks
title_sort Finite-dimensional pointed or copointed Hopf algebras over affine racks
dc.creator.none.fl_str_mv Garcia Iglesias, Agustin
Vay, Cristian Damian
author Garcia Iglesias, Agustin
author_facet Garcia Iglesias, Agustin
Vay, Cristian Damian
author_role author
author2 Vay, Cristian Damian
author2_role author
dc.subject.none.fl_str_mv Pointed Hopf Algebras
Copointed Hopf Algebras
Affine Racks
Nichols Algebras
topic Pointed Hopf Algebras
Copointed Hopf Algebras
Affine Racks
Nichols Algebras
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 study the pointed or copointed liftings of Nichols algebras associated to affine racks and constant cocycles for any finite group admitting a principal YD-realization of these racks. In the copointed case we complete the classification for the six affine racks whose Nichols algebra is known to be of finite dimension. In the pointed case our method allows us to finish four of them. In all of the cases the Hopf algebras obtained turn out to be cocycle deformations of their associated graded Hopf algebras. All of them are new examples of finite-dimensional copointed or pointed Hopf algebras over non-abelian groups.
Fil: Garcia Iglesias, Agustin. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentina
Fil: Vay, Cristian Damian. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentina. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina
description We study the pointed or copointed liftings of Nichols algebras associated to affine racks and constant cocycles for any finite group admitting a principal YD-realization of these racks. In the copointed case we complete the classification for the six affine racks whose Nichols algebra is known to be of finite dimension. In the pointed case our method allows us to finish four of them. In all of the cases the Hopf algebras obtained turn out to be cocycle deformations of their associated graded Hopf algebras. All of them are new examples of finite-dimensional copointed or pointed Hopf algebras over non-abelian groups.
publishDate 2014
dc.date.none.fl_str_mv 2014-01
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/11336/31951
Vay, Cristian Damian; Garcia Iglesias, Agustin; Finite-dimensional pointed or copointed Hopf algebras over affine racks; Academic Press Inc Elsevier Science; Journal Of Algebra; 397; 1-2014; 379-406
0021-8693
CONICET Digital
CONICET
url http://hdl.handle.net/11336/31951
identifier_str_mv Vay, Cristian Damian; Garcia Iglesias, Agustin; Finite-dimensional pointed or copointed Hopf algebras over affine racks; Academic Press Inc Elsevier Science; Journal Of Algebra; 397; 1-2014; 379-406
0021-8693
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1016/j.jalgebra.2013.09.009
info:eu-repo/semantics/altIdentifier/url/http://www.sciencedirect.com/science/article/pii/S0021869313004985
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
application/pdf
dc.publisher.none.fl_str_mv Academic Press Inc Elsevier Science
publisher.none.fl_str_mv Academic Press Inc Elsevier Science
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 13.070432

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