Finite quantum groups and quantum permutation groups

Autores
Banica, Teodor; Bichon, Julien; Natale, Sonia Lujan
Año de publicación
2012
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We give examples of finite quantum permutation groups which arise from the twisting construction or as bicrossed products associated to exact factorizations in finite groups. We also give examples of finite quantum groups which are not quantum permutation groups: one such example occurs as a split abelian extension associated to the exact factorization S_4 = Z_4 S_3 and has dimension 24. We show that, in fact, this is the smallest possible dimension that a non quantum permutation group can have.
Fil: Banica, Teodor. No especifíca;
Fil: Bichon, Julien. No especifíca;
Fil: Natale, Sonia Lujan. Université de Cergy; Francia. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. Universite Blaise Pascal; Francia. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Materia
semisimple Hopf algebra
quantum permutation group
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:11336/269401
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/269401
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Finite quantum groups and quantum permutation groupsBanica, TeodorBichon, JulienNatale, Sonia Lujansemisimple Hopf algebraquantum permutation grouphttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We give examples of finite quantum permutation groups which arise from the twisting construction or as bicrossed products associated to exact factorizations in finite groups. We also give examples of finite quantum groups which are not quantum permutation groups: one such example occurs as a split abelian extension associated to the exact factorization S_4 = Z_4 S_3 and has dimension 24. We show that, in fact, this is the smallest possible dimension that a non quantum permutation group can have.Fil: Banica, Teodor. No especifíca;Fil: Bichon, Julien. No especifíca;Fil: Natale, Sonia Lujan. Université de Cergy; Francia. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. Universite Blaise Pascal; Francia. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaAcademic Press Inc Elsevier Science2012-03info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/269401Banica, Teodor; Bichon, Julien; Natale, Sonia Lujan; Finite quantum groups and quantum permutation groups; Academic Press Inc Elsevier Science; Advances in Mathematics; 229; 3-2012; 3320-33380001-8708CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1104.1400v1info:eu-repo/semantics/altIdentifier/doi/10.48550/arXiv.1104.1400info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-22T11:16:19Zoai:ri.conicet.gov.ar:11336/269401instacron: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:34982025-10-22 11:16:20.293CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Finite quantum groups and quantum permutation groups
title Finite quantum groups and quantum permutation groups
spellingShingle Finite quantum groups and quantum permutation groups
Banica, Teodor
semisimple Hopf algebra
quantum permutation group
title_short Finite quantum groups and quantum permutation groups
title_full Finite quantum groups and quantum permutation groups
title_fullStr Finite quantum groups and quantum permutation groups
title_full_unstemmed Finite quantum groups and quantum permutation groups
title_sort Finite quantum groups and quantum permutation groups
dc.creator.none.fl_str_mv Banica, Teodor
Bichon, Julien
Natale, Sonia Lujan
author Banica, Teodor
author_facet Banica, Teodor
Bichon, Julien
Natale, Sonia Lujan
author_role author
author2 Bichon, Julien
Natale, Sonia Lujan
author2_role author
author
dc.subject.none.fl_str_mv semisimple Hopf algebra
quantum permutation group
topic semisimple Hopf algebra
quantum permutation group
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 give examples of finite quantum permutation groups which arise from the twisting construction or as bicrossed products associated to exact factorizations in finite groups. We also give examples of finite quantum groups which are not quantum permutation groups: one such example occurs as a split abelian extension associated to the exact factorization S_4 = Z_4 S_3 and has dimension 24. We show that, in fact, this is the smallest possible dimension that a non quantum permutation group can have.
Fil: Banica, Teodor. No especifíca;
Fil: Bichon, Julien. No especifíca;
Fil: Natale, Sonia Lujan. Université de Cergy; Francia. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. Universite Blaise Pascal; Francia. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
description We give examples of finite quantum permutation groups which arise from the twisting construction or as bicrossed products associated to exact factorizations in finite groups. We also give examples of finite quantum groups which are not quantum permutation groups: one such example occurs as a split abelian extension associated to the exact factorization S_4 = Z_4 S_3 and has dimension 24. We show that, in fact, this is the smallest possible dimension that a non quantum permutation group can have.
publishDate 2012
dc.date.none.fl_str_mv 2012-03
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/11336/269401
Banica, Teodor; Bichon, Julien; Natale, Sonia Lujan; Finite quantum groups and quantum permutation groups; Academic Press Inc Elsevier Science; Advances in Mathematics; 229; 3-2012; 3320-3338
0001-8708
CONICET Digital
CONICET
url http://hdl.handle.net/11336/269401
identifier_str_mv Banica, Teodor; Bichon, Julien; Natale, Sonia Lujan; Finite quantum groups and quantum permutation groups; Academic Press Inc Elsevier Science; Advances in Mathematics; 229; 3-2012; 3320-3338
0001-8708
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1104.1400v1
info:eu-repo/semantics/altIdentifier/doi/10.48550/arXiv.1104.1400
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 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 12.982451

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