Nichols algebras with many cubic relations

Autores
Heckenberger, I.; Lochmann, A.; Vendramin, Claudio Leandro
Año de publicación
2015
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Nichols algebras of group type with many cubic relations are classified under a technical assumption on the structure of Hurwitz orbits of the third power of the underlying indecomposable rack. All such Nichols algebras are finite-dimensional, and their Hilbert series have a factorization into quantum integers. Also, all known finite-dimensional elementary Nichols algebras turn out to have many cubic relations. The technical assumption of our theorem can be removed if a conjecture in the theory of cellular automata can be proven.
Fil: Heckenberger, I.. Philipps Universität Marburg; Alemania
Fil: Lochmann, A.. Philipps Universität Marburg; Alemania
Fil: Vendramin, Claudio Leandro. Philipps Universität Marburg; Alemania. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Materia
Nichols algebras
Hurwitz orbits
Braid group
Cellular automata
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:11336/59632
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/59632
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Nichols algebras with many cubic relationsHeckenberger, I.Lochmann, A.Vendramin, Claudio LeandroNichols algebrasHurwitz orbitsBraid groupCellular automatahttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Nichols algebras of group type with many cubic relations are classified under a technical assumption on the structure of Hurwitz orbits of the third power of the underlying indecomposable rack. All such Nichols algebras are finite-dimensional, and their Hilbert series have a factorization into quantum integers. Also, all known finite-dimensional elementary Nichols algebras turn out to have many cubic relations. The technical assumption of our theorem can be removed if a conjecture in the theory of cellular automata can be proven.Fil: Heckenberger, I.. Philipps Universität Marburg; AlemaniaFil: Lochmann, A.. Philipps Universität Marburg; AlemaniaFil: Vendramin, Claudio Leandro. Philipps Universität Marburg; Alemania. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaAmerican Mathematical Society2015-12info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/59632Heckenberger, I.; Lochmann, A.; Vendramin, Claudio Leandro; Nichols algebras with many cubic relations; American Mathematical Society; Transactions Of The American Mathematical Society; 367; 9; 12-2015; 6315-63560002-9947CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/http://arxiv.org/abs/1212.4330info:eu-repo/semantics/altIdentifier/doi/10.1090/S0002-9947-2015-06231-Xinfo:eu-repo/semantics/altIdentifier/url/http://www.ams.org/journals/tran/2015-367-09/S0002-9947-2015-06231-X/info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-29T12:30:29Zoai:ri.conicet.gov.ar:11336/59632instacron: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:34982025-10-29 12:30:29.45CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Nichols algebras with many cubic relations
title Nichols algebras with many cubic relations
spellingShingle Nichols algebras with many cubic relations
Heckenberger, I.
Nichols algebras
Hurwitz orbits
Braid group
Cellular automata
title_short Nichols algebras with many cubic relations
title_full Nichols algebras with many cubic relations
title_fullStr Nichols algebras with many cubic relations
title_full_unstemmed Nichols algebras with many cubic relations
title_sort 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 Nichols algebras
Hurwitz orbits
Braid group
Cellular automata
topic Nichols algebras
Hurwitz orbits
Braid group
Cellular automata
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv Nichols algebras of group type with many cubic relations are classified under a technical assumption on the structure of Hurwitz orbits of the third power of the underlying indecomposable rack. All such Nichols algebras are finite-dimensional, and their Hilbert series have a factorization into quantum integers. Also, all known finite-dimensional elementary Nichols algebras turn out to have many cubic relations. The technical assumption of our theorem can be removed if a conjecture in the theory of cellular automata can be proven.
Fil: Heckenberger, I.. Philipps Universität Marburg; Alemania
Fil: Lochmann, A.. Philipps Universität Marburg; Alemania
Fil: Vendramin, Claudio Leandro. Philipps Universität Marburg; Alemania. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
description Nichols algebras of group type with many cubic relations are classified under a technical assumption on the structure of Hurwitz orbits of the third power of the underlying indecomposable rack. All such Nichols algebras are finite-dimensional, and their Hilbert series have a factorization into quantum integers. Also, all known finite-dimensional elementary Nichols algebras turn out to have many cubic relations. The technical assumption of our theorem can be removed if a conjecture in the theory of cellular automata can be proven.
publishDate 2015
dc.date.none.fl_str_mv 2015-12
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/11336/59632
Heckenberger, I.; Lochmann, A.; Vendramin, Claudio Leandro; Nichols algebras with many cubic relations; American Mathematical Society; Transactions Of The American Mathematical Society; 367; 9; 12-2015; 6315-6356
0002-9947
CONICET Digital
CONICET
url http://hdl.handle.net/11336/59632
identifier_str_mv Heckenberger, I.; Lochmann, A.; Vendramin, Claudio Leandro; Nichols algebras with many cubic relations; American Mathematical Society; Transactions Of The American Mathematical Society; 367; 9; 12-2015; 6315-6356
0002-9947
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/http://arxiv.org/abs/1212.4330
info:eu-repo/semantics/altIdentifier/doi/10.1090/S0002-9947-2015-06231-X
info:eu-repo/semantics/altIdentifier/url/http://www.ams.org/journals/tran/2015-367-09/S0002-9947-2015-06231-X/
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 American Mathematical Society
publisher.none.fl_str_mv American 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
_version_ 1847427246046838784
score 13.10058

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