A classification of Nichols algebras of semisimple Yetter-Drinfeld modules over non-abelian groups

Autores
Heckenberger, István; Vendramin, Claudio Leandro
Año de publicación
2017
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Over fields of arbitrary characteristic we classify all braid-indecomposable tuples of at least two absolutely simple Yetter-Drinfeld modules over non-abelian groups such that the group is generated by the support of the tuple and the Nichols algebra of the tuple is finite-dimensional. Such tuples are classified in terms of analogs of Dynkin diagrams which encode much information about the Yetter-Drinfeld modules. We also compute the dimensions of these finite-dimensional Nichols algebras. Our proof uses essentially theWeyl groupoid of a tuple of simple Yetter-Drinfeld modules and our previous result on pairs.
Fil: Heckenberger, István. Philipps Universitat Marburg; Alemania
Fil: Vendramin, Claudio Leandro. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina
Materia
Hopf Algebra
Nichols Algebra
Weyl Groupoid
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:11336/55447
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/55447
network_acronym_str CONICETDig
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network_name_str CONICET Digital (CONICET)
spelling A classification of Nichols algebras of semisimple Yetter-Drinfeld modules over non-abelian groupsHeckenberger, IstvánVendramin, Claudio LeandroHopf AlgebraNichols AlgebraWeyl Groupoidhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Over fields of arbitrary characteristic we classify all braid-indecomposable tuples of at least two absolutely simple Yetter-Drinfeld modules over non-abelian groups such that the group is generated by the support of the tuple and the Nichols algebra of the tuple is finite-dimensional. Such tuples are classified in terms of analogs of Dynkin diagrams which encode much information about the Yetter-Drinfeld modules. We also compute the dimensions of these finite-dimensional Nichols algebras. Our proof uses essentially theWeyl groupoid of a tuple of simple Yetter-Drinfeld modules and our previous result on pairs.Fil: Heckenberger, István. Philipps Universitat Marburg; AlemaniaFil: Vendramin, Claudio Leandro. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; ArgentinaEuropean Mathematical Society2017-02info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/55447Heckenberger, István; Vendramin, Claudio Leandro; A classification of Nichols algebras of semisimple Yetter-Drinfeld modules over non-abelian groups; European Mathematical Society; Journal of the European Mathematical Society; 19; 2; 2-2017; 299-3561435-9855CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.4171/JEMS/667info:eu-repo/semantics/altIdentifier/url/http://www.ems-ph.org/journals/show_abstract.php?issn=1435-9855&vol=19&iss=2&rank=1info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T09:41:38Zoai:ri.conicet.gov.ar:11336/55447instacron: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 09:41:38.801CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv A classification of Nichols algebras of semisimple Yetter-Drinfeld modules over non-abelian groups
title A classification of Nichols algebras of semisimple Yetter-Drinfeld modules over non-abelian groups
spellingShingle A classification of Nichols algebras of semisimple Yetter-Drinfeld modules over non-abelian groups
Heckenberger, István
Hopf Algebra
Nichols Algebra
Weyl Groupoid
title_short A classification of Nichols algebras of semisimple Yetter-Drinfeld modules over non-abelian groups
title_full A classification of Nichols algebras of semisimple Yetter-Drinfeld modules over non-abelian groups
title_fullStr A classification of Nichols algebras of semisimple Yetter-Drinfeld modules over non-abelian groups
title_full_unstemmed A classification of Nichols algebras of semisimple Yetter-Drinfeld modules over non-abelian groups
title_sort A classification of Nichols algebras of semisimple Yetter-Drinfeld modules over non-abelian groups
dc.creator.none.fl_str_mv Heckenberger, István
Vendramin, Claudio Leandro
author Heckenberger, István
author_facet Heckenberger, István
Vendramin, Claudio Leandro
author_role author
author2 Vendramin, Claudio Leandro
author2_role author
dc.subject.none.fl_str_mv Hopf Algebra
Nichols Algebra
Weyl Groupoid
topic Hopf Algebra
Nichols Algebra
Weyl Groupoid
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv Over fields of arbitrary characteristic we classify all braid-indecomposable tuples of at least two absolutely simple Yetter-Drinfeld modules over non-abelian groups such that the group is generated by the support of the tuple and the Nichols algebra of the tuple is finite-dimensional. Such tuples are classified in terms of analogs of Dynkin diagrams which encode much information about the Yetter-Drinfeld modules. We also compute the dimensions of these finite-dimensional Nichols algebras. Our proof uses essentially theWeyl groupoid of a tuple of simple Yetter-Drinfeld modules and our previous result on pairs.
Fil: Heckenberger, István. Philipps Universitat Marburg; Alemania
Fil: Vendramin, Claudio Leandro. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina
description Over fields of arbitrary characteristic we classify all braid-indecomposable tuples of at least two absolutely simple Yetter-Drinfeld modules over non-abelian groups such that the group is generated by the support of the tuple and the Nichols algebra of the tuple is finite-dimensional. Such tuples are classified in terms of analogs of Dynkin diagrams which encode much information about the Yetter-Drinfeld modules. We also compute the dimensions of these finite-dimensional Nichols algebras. Our proof uses essentially theWeyl groupoid of a tuple of simple Yetter-Drinfeld modules and our previous result on pairs.
publishDate 2017
dc.date.none.fl_str_mv 2017-02
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/11336/55447
Heckenberger, István; Vendramin, Claudio Leandro; A classification of Nichols algebras of semisimple Yetter-Drinfeld modules over non-abelian groups; European Mathematical Society; Journal of the European Mathematical Society; 19; 2; 2-2017; 299-356
1435-9855
CONICET Digital
CONICET
url http://hdl.handle.net/11336/55447
identifier_str_mv Heckenberger, István; Vendramin, Claudio Leandro; A classification of Nichols algebras of semisimple Yetter-Drinfeld modules over non-abelian groups; European Mathematical Society; Journal of the European Mathematical Society; 19; 2; 2-2017; 299-356
1435-9855
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.4171/JEMS/667
info:eu-repo/semantics/altIdentifier/url/http://www.ems-ph.org/journals/show_abstract.php?issn=1435-9855&vol=19&iss=2&rank=1
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 13.070432

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