Nichols algebras over groups with finite root system of rank two II

Autores
Heckenberger, István; Vendramin, Claudio Leandro
Año de publicación
2014
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We classify all non-abelian groups G for which there exists a pair (V,W) of absolutely simple Yetter–Drinfeld modules over G such that the Nichols algebra of the direct sum of V and W is finite-dimensional, under two assumptions: the square of the braiding between V and W is not the identity, and G is generated by the support of V and W. As a corollary, we prove that the dimensions of such V and W are at most six. As a tool we use the Weyl groupoid of (V,W).
Fil: Heckenberger, István. Philipps Universität Marburg; Alemania
Fil: Vendramin, Claudio Leandro. Philipps Universität Marburg; Alemania. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Materia
Nichols algebras
Weyl groupoids
Root systems
Hopf 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:11336/33077
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/33077
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Nichols algebras over groups with finite root system of rank two IIHeckenberger, IstvánVendramin, Claudio LeandroNichols algebrasWeyl groupoidsRoot systemsHopf algebrashttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We classify all non-abelian groups G for which there exists a pair (V,W) of absolutely simple Yetter–Drinfeld modules over G such that the Nichols algebra of the direct sum of V and W is finite-dimensional, under two assumptions: the square of the braiding between V and W is not the identity, and G is generated by the support of V and W. As a corollary, we prove that the dimensions of such V and W are at most six. As a tool we use the Weyl groupoid of (V,W).Fil: Heckenberger, István. Philipps Universität Marburg; AlemaniaFil: Vendramin, Claudio Leandro. Philipps Universität Marburg; Alemania. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaDe Gruyter2014-05info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/33077Heckenberger, István; Vendramin, Claudio Leandro; Nichols algebras over groups with finite root system of rank two II; De Gruyter; Journal Of Group Theory; 17; 6; 5-2014; 1009-10341433-58831435-4446CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1515/jgth-2014-0024info:eu-repo/semantics/altIdentifier/url/https://www.degruyter.com/view/j/jgth.ahead-of-print/jgth-2014-0024/jgth-2014-0024.xmlinfo:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T09:50:26Zoai:ri.conicet.gov.ar:11336/33077instacron: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 09:50:26.353CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Nichols algebras over groups with finite root system of rank two II
title Nichols algebras over groups with finite root system of rank two II
spellingShingle Nichols algebras over groups with finite root system of rank two II
Heckenberger, István
Nichols algebras
Weyl groupoids
Root systems
Hopf algebras
title_short Nichols algebras over groups with finite root system of rank two II
title_full Nichols algebras over groups with finite root system of rank two II
title_fullStr Nichols algebras over groups with finite root system of rank two II
title_full_unstemmed Nichols algebras over groups with finite root system of rank two II
title_sort Nichols algebras over groups with finite root system of rank two II
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 Nichols algebras
Weyl groupoids
Root systems
Hopf algebras
topic Nichols algebras
Weyl groupoids
Root systems
Hopf 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 classify all non-abelian groups G for which there exists a pair (V,W) of absolutely simple Yetter–Drinfeld modules over G such that the Nichols algebra of the direct sum of V and W is finite-dimensional, under two assumptions: the square of the braiding between V and W is not the identity, and G is generated by the support of V and W. As a corollary, we prove that the dimensions of such V and W are at most six. As a tool we use the Weyl groupoid of (V,W).
Fil: Heckenberger, István. Philipps Universität Marburg; Alemania
Fil: Vendramin, Claudio Leandro. Philipps Universität Marburg; Alemania. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
description We classify all non-abelian groups G for which there exists a pair (V,W) of absolutely simple Yetter–Drinfeld modules over G such that the Nichols algebra of the direct sum of V and W is finite-dimensional, under two assumptions: the square of the braiding between V and W is not the identity, and G is generated by the support of V and W. As a corollary, we prove that the dimensions of such V and W are at most six. As a tool we use the Weyl groupoid of (V,W).
publishDate 2014
dc.date.none.fl_str_mv 2014-05
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/11336/33077
Heckenberger, István; Vendramin, Claudio Leandro; Nichols algebras over groups with finite root system of rank two II; De Gruyter; Journal Of Group Theory; 17; 6; 5-2014; 1009-1034
1433-5883
1435-4446
CONICET Digital
CONICET
url http://hdl.handle.net/11336/33077
identifier_str_mv Heckenberger, István; Vendramin, Claudio Leandro; Nichols algebras over groups with finite root system of rank two II; De Gruyter; Journal Of Group Theory; 17; 6; 5-2014; 1009-1034
1433-5883
1435-4446
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1515/jgth-2014-0024
info:eu-repo/semantics/altIdentifier/url/https://www.degruyter.com/view/j/jgth.ahead-of-print/jgth-2014-0024/jgth-2014-0024.xml
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 De Gruyter
publisher.none.fl_str_mv De Gruyter
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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