A presentation by generators and relations of Nichols algebras of diagonal type and convex orders on root systems

We obtain a presentation by generators and relations of any Nichols algebra of diagonal type with finite root system. We prove that the defining ideal is finitely generated. The proof is based on Kharchenko's theory of PBW bases of Lyndon words. We prove that the lexicographic order on Lyndon w...

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Detalles Bibliográficos
Autor: Angiono, Iván Ezequiel
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2015
País:Argentina
Institución:Consejo Nacional de Investigaciones Científicas y Técnicas
Repositorio:CONICET Digital (CONICET)
Idioma:inglés
OAI Identifier:oai:ri.conicet.gov.ar:11336/53098
Acceso en línea:http://hdl.handle.net/11336/53098
Access Level:acceso abierto
Palabra clave:Nichols Algebras
Pointed Hopf Algebras
Quantized Enveloping Algebras
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
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spelling A presentation by generators and relations of Nichols algebras of diagonal type and convex orders on root systemsAngiono, Iván EzequielNichols AlgebrasPointed Hopf AlgebrasQuantized Enveloping Algebrashttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We obtain a presentation by generators and relations of any Nichols algebra of diagonal type with finite root system. We prove that the defining ideal is finitely generated. The proof is based on Kharchenko's theory of PBW bases of Lyndon words. We prove that the lexicographic order on Lyndon words is convex for PBW generators and so the PBW basis is orthogonal with respect to the canonical non-degenerate form associated to the Nichols algebra.Fil: Angiono, Iván Ezequiel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; ArgentinaEuropean Mathematical Society2015-10-29info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/53098Angiono, Iván Ezequiel; A presentation by generators and relations of Nichols algebras of diagonal type and convex orders on root systems; European Mathematical Society; Journal of the European Mathematical Society; 17; 10; 29-10-2015; 2643-26711435-9855CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/http://www.ems-ph.org/journals/show_abstract.php?issn=1435-9855&vol=17&iss=10&rank=7info:eu-repo/semantics/altIdentifier/doi/10.4171/JEMS/567info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2024-05-08T13:47:14Zoai:ri.conicet.gov.ar:11336/53098instacron: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 13:47:15.04CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv A presentation by generators and relations of Nichols algebras of diagonal type and convex orders on root systems
title A presentation by generators and relations of Nichols algebras of diagonal type and convex orders on root systems
spellingShingle A presentation by generators and relations of Nichols algebras of diagonal type and convex orders on root systems
Angiono, Iván Ezequiel
Nichols Algebras
Pointed Hopf Algebras
Quantized Enveloping Algebras
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
title_short A presentation by generators and relations of Nichols algebras of diagonal type and convex orders on root systems
title_full A presentation by generators and relations of Nichols algebras of diagonal type and convex orders on root systems
title_fullStr A presentation by generators and relations of Nichols algebras of diagonal type and convex orders on root systems
title_full_unstemmed A presentation by generators and relations of Nichols algebras of diagonal type and convex orders on root systems
title_sort A presentation by generators and relations of Nichols algebras of diagonal type and convex orders on root systems
dc.creator.none.fl_str_mv Angiono, Iván Ezequiel
author Angiono, Iván Ezequiel
author_facet Angiono, Iván Ezequiel
author_role author
dc.subject.none.fl_str_mv Nichols Algebras
Pointed Hopf Algebras
Quantized Enveloping Algebras
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
topic Nichols Algebras
Pointed Hopf Algebras
Quantized Enveloping Algebras
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
description We obtain a presentation by generators and relations of any Nichols algebra of diagonal type with finite root system. We prove that the defining ideal is finitely generated. The proof is based on Kharchenko's theory of PBW bases of Lyndon words. We prove that the lexicographic order on Lyndon words is convex for PBW generators and so the PBW basis is orthogonal with respect to the canonical non-degenerate form associated to the Nichols algebra.
publishDate 2015
dc.date.none.fl_str_mv 2015-10-29
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/11336/53098
Angiono, Iván Ezequiel; A presentation by generators and relations of Nichols algebras of diagonal type and convex orders on root systems; European Mathematical Society; Journal of the European Mathematical Society; 17; 10; 29-10-2015; 2643-2671
1435-9855
CONICET Digital
CONICET
url http://hdl.handle.net/11336/53098
identifier_str_mv Angiono, Iván Ezequiel; A presentation by generators and relations of Nichols algebras of diagonal type and convex orders on root systems; European Mathematical Society; Journal of the European Mathematical Society; 17; 10; 29-10-2015; 2643-2671
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/url/http://www.ems-ph.org/journals/show_abstract.php?issn=1435-9855&vol=17&iss=10&rank=7
info:eu-repo/semantics/altIdentifier/doi/10.4171/JEMS/567
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by/2.5/ar/
dc.format.none.fl_str_mv application/pdf
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
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 15.812429

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