On Nichols algebras of diagonal type

Autores
Angiono, Iván Ezequiel
Año de publicación
2013
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We give an explicit and essentially minimal list of defining relations of a Nichols algebra of diagonal type with finite root system. This list contains the well-known quantum Serre relations but also many new variations. A conjecture by Andruskiewitsch and Schneider states that any finite-dimensional pointed Hopf algebra over an algebraically closed field of characteristic zero is generated as an algebra by its group-like and skew-primitive elements. As an application of our main result, we prove the conjecture when the group of group-like elements is abelian.
Fil: Angiono, Iván Ezequiel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Córdoba. Centro de Investigación y Estudios de Matemática de Córdoba(p); Argentina
Materia
Hopf Algebras
Nichols 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:11336/11345
Acceder
id CONICETDig_7de3a8d949ec184daa15237b33152075
oai_identifier_str oai:ri.conicet.gov.ar:11336/11345
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling On Nichols algebras of diagonal typeAngiono, Iván EzequielHopf AlgebrasNichols Algebrashttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We give an explicit and essentially minimal list of defining relations of a Nichols algebra of diagonal type with finite root system. This list contains the well-known quantum Serre relations but also many new variations. A conjecture by Andruskiewitsch and Schneider states that any finite-dimensional pointed Hopf algebra over an algebraically closed field of characteristic zero is generated as an algebra by its group-like and skew-primitive elements. As an application of our main result, we prove the conjecture when the group of group-like elements is abelian.Fil: Angiono, Iván Ezequiel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Córdoba. Centro de Investigación y Estudios de Matemática de Córdoba(p); Argentinade Gruyter2013-11info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/zipapplication/pdfhttp://hdl.handle.net/11336/11345Angiono, Iván Ezequiel; On Nichols algebras of diagonal type; de Gruyter; Journal Fur Die Reine Und Angewandte Mathematik; 683; 11-2013; 189-2510075-4102enginfo:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1104.0268info:eu-repo/semantics/altIdentifier/url/https://www.degruyter.com/view/j/crelle.2013.2013.issue-683/crelle-2011-0008/crelle-2011-0008.xml?format=INTinfo:eu-repo/semantics/altIdentifier/doi/10.1515/crelle-2011-0008info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T09:58:32Zoai:ri.conicet.gov.ar:11336/11345instacron: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:34982025-09-03 09:58:32.83CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv On Nichols algebras of diagonal type
title On Nichols algebras of diagonal type
spellingShingle On Nichols algebras of diagonal type
Angiono, Iván Ezequiel
Hopf Algebras
Nichols Algebras
title_short On Nichols algebras of diagonal type
title_full On Nichols algebras of diagonal type
title_fullStr On Nichols algebras of diagonal type
title_full_unstemmed On Nichols algebras of diagonal type
title_sort On Nichols algebras of diagonal type
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 Hopf Algebras
Nichols Algebras
topic Hopf Algebras
Nichols 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 give an explicit and essentially minimal list of defining relations of a Nichols algebra of diagonal type with finite root system. This list contains the well-known quantum Serre relations but also many new variations. A conjecture by Andruskiewitsch and Schneider states that any finite-dimensional pointed Hopf algebra over an algebraically closed field of characteristic zero is generated as an algebra by its group-like and skew-primitive elements. As an application of our main result, we prove the conjecture when the group of group-like elements is abelian.
Fil: Angiono, Iván Ezequiel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Córdoba. Centro de Investigación y Estudios de Matemática de Córdoba(p); Argentina
description We give an explicit and essentially minimal list of defining relations of a Nichols algebra of diagonal type with finite root system. This list contains the well-known quantum Serre relations but also many new variations. A conjecture by Andruskiewitsch and Schneider states that any finite-dimensional pointed Hopf algebra over an algebraically closed field of characteristic zero is generated as an algebra by its group-like and skew-primitive elements. As an application of our main result, we prove the conjecture when the group of group-like elements is abelian.
publishDate 2013
dc.date.none.fl_str_mv 2013-11
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/11336/11345
Angiono, Iván Ezequiel; On Nichols algebras of diagonal type; de Gruyter; Journal Fur Die Reine Und Angewandte Mathematik; 683; 11-2013; 189-251
0075-4102
url http://hdl.handle.net/11336/11345
identifier_str_mv Angiono, Iván Ezequiel; On Nichols algebras of diagonal type; de Gruyter; Journal Fur Die Reine Und Angewandte Mathematik; 683; 11-2013; 189-251
0075-4102
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1104.0268
info:eu-repo/semantics/altIdentifier/url/https://www.degruyter.com/view/j/crelle.2013.2013.issue-683/crelle-2011-0008/crelle-2011-0008.xml?format=INT
info:eu-repo/semantics/altIdentifier/doi/10.1515/crelle-2011-0008
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/zip
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
_version_ 1842269526880681984
score 13.13397

Publicaciones similares