Braided racks, Hurwitz actions and Nichols algebras with many cubic relations

We classify Nichols algebras of irreducible Yetter-Drinfeld modules over groups such that the underlying rack is braided and the homogeneous component of degree three of the Nichols algebra satisfies a given inequality. This assumption turns out to be equivalent to a factorization assumption on the...

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Detalles Bibliográficos
Autores: Heckenberger, I., Lochmann, A., Vendramin, Claudio Leandro
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2012
País:Argentina
Institución:Consejo Nacional de Investigaciones Científicas y Técnicas
Repositorio:CONICET Digital (CONICET)
Idioma:inglés
OAI Identifier:oai:ri.conicet.gov.ar:11336/217391
Acceso en línea:http://hdl.handle.net/11336/217391
Access Level:acceso abierto
Palabra clave:3-TRANSPOSITION GROUP
HOPF ALGEBRA
HURWITZ ACTION
NICHOLS ALGEBRA
RACK
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
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spelling Braided racks, Hurwitz actions and Nichols algebras with many cubic relationsHeckenberger, I.Lochmann, A.Vendramin, Claudio Leandro3-TRANSPOSITION GROUPHOPF ALGEBRAHURWITZ ACTIONNICHOLS ALGEBRARACKhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We classify Nichols algebras of irreducible Yetter-Drinfeld modules over groups such that the underlying rack is braided and the homogeneous component of degree three of the Nichols algebra satisfies a given inequality. This assumption turns out to be equivalent to a factorization assumption on the Hilbert series. Besides the known Nichols algebras we obtain a new example. Our method is based on a combinatorial invariant of the Hurwitz orbits with respect to the action of the braid group on three strands.Fil: Heckenberger, I.. Philipps-Universität Marburg; AlemaniaFil: Lochmann, A.. Philipps-Universität Marburg; AlemaniaFil: Vendramin, Claudio Leandro. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; ArgentinaSpringer2012-03info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/217391Heckenberger, I.; Lochmann, A.; Vendramin, Claudio Leandro; Braided racks, Hurwitz actions and Nichols algebras with many cubic relations; Springer; Transformation Groups; 17; 1; 3-2012; 157-1941083-4362CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007/s00031-012-9176-7info:eu-repo/semantics/altIdentifier/doi/10.1007/s00031-012-9176-7info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2024-05-08T14:06:03Zoai:ri.conicet.gov.ar:11336/217391instacron: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:34982024-05-08 14:06:03.746CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Braided racks, Hurwitz actions and Nichols algebras with many cubic relations
title Braided racks, Hurwitz actions and Nichols algebras with many cubic relations
spellingShingle Braided racks, Hurwitz actions and Nichols algebras with many cubic relations
Heckenberger, I.
3-TRANSPOSITION GROUP
HOPF ALGEBRA
HURWITZ ACTION
NICHOLS ALGEBRA
RACK
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
title_short Braided racks, Hurwitz actions and Nichols algebras with many cubic relations
title_full Braided racks, Hurwitz actions and Nichols algebras with many cubic relations
title_fullStr Braided racks, Hurwitz actions and Nichols algebras with many cubic relations
title_full_unstemmed Braided racks, Hurwitz actions and Nichols algebras with many cubic relations
title_sort Braided racks, Hurwitz actions and Nichols algebras with many cubic relations
dc.creator.none.fl_str_mv Heckenberger, I.
Lochmann, A.
Vendramin, Claudio Leandro
author Heckenberger, I.
author_facet Heckenberger, I.
Lochmann, A.
Vendramin, Claudio Leandro
author_role author
author2 Lochmann, A.
Vendramin, Claudio Leandro
author2_role author
author
dc.subject.none.fl_str_mv 3-TRANSPOSITION GROUP
HOPF ALGEBRA
HURWITZ ACTION
NICHOLS ALGEBRA
RACK
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
topic 3-TRANSPOSITION GROUP
HOPF ALGEBRA
HURWITZ ACTION
NICHOLS ALGEBRA
RACK
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
description We classify Nichols algebras of irreducible Yetter-Drinfeld modules over groups such that the underlying rack is braided and the homogeneous component of degree three of the Nichols algebra satisfies a given inequality. This assumption turns out to be equivalent to a factorization assumption on the Hilbert series. Besides the known Nichols algebras we obtain a new example. Our method is based on a combinatorial invariant of the Hurwitz orbits with respect to the action of the braid group on three strands.
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/11336/217391
Heckenberger, I.; Lochmann, A.; Vendramin, Claudio Leandro; Braided racks, Hurwitz actions and Nichols algebras with many cubic relations; Springer; Transformation Groups; 17; 1; 3-2012; 157-194
1083-4362
CONICET Digital
CONICET
url http://hdl.handle.net/11336/217391
identifier_str_mv Heckenberger, I.; Lochmann, A.; Vendramin, Claudio Leandro; Braided racks, Hurwitz actions and Nichols algebras with many cubic relations; Springer; Transformation Groups; 17; 1; 3-2012; 157-194
1083-4362
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://link.springer.com/article/10.1007/s00031-012-9176-7
info:eu-repo/semantics/altIdentifier/doi/10.1007/s00031-012-9176-7
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 Springer
publisher.none.fl_str_mv Springer
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
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 15,811543

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