Finite-dimensional Nichols algebras over dual Radford algebras

Autores
Bagio, D.; García, Gastón Andrés; Jury Giraldi, Joao Matheus; Márquez, O.
Año de publicación
2021
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
For n, m ∈ N, let Hn,m be the dual of the Radford algebra of dimension n 2m. We present new finite-dimensional Nichols algebras arising from the study of simple Yetter-Drinfeld modules over Hn,m. Along the way, we describe the simple objects in Hn,m Hn,m YD and their projective envelopes. Then, we determine those simple modules that give rise to finite-dimensional Nichols algebras for the case n = 2. There are 18 possible cases. We present by generators and relations the corresponding Nichols algebras on five of these eighteen cases. As an application, we characterize finite-dimensional Nichols algebras over indecomposable modules for n = 2 = m and n = 2, m = 3, which recovers some results of the second and third author in the former case, and of Xiong in the latter.
Fil: Bagio, D.. Universidade Federal de Santa Maria; Brasil
Fil: García, Gastón Andrés. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata; Argentina
Fil: Jury Giraldi, Joao Matheus. Universidade Federal de Santa Maria; Brasil
Fil: Márquez, O.. Universidade Federal de Santa Maria; Brasil
Materia
DUAL RADFORD HOPF ALGEBRA
HOPF ALGEBRA
NICHOLS ALGEBRA
STANDARD FILTRATION
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:11336/150434
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/150434
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Finite-dimensional Nichols algebras over dual Radford algebrasBagio, D.García, Gastón AndrésJury Giraldi, Joao MatheusMárquez, O.DUAL RADFORD HOPF ALGEBRAHOPF ALGEBRANICHOLS ALGEBRASTANDARD FILTRATIONhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1For n, m ∈ N, let Hn,m be the dual of the Radford algebra of dimension n 2m. We present new finite-dimensional Nichols algebras arising from the study of simple Yetter-Drinfeld modules over Hn,m. Along the way, we describe the simple objects in Hn,m Hn,m YD and their projective envelopes. Then, we determine those simple modules that give rise to finite-dimensional Nichols algebras for the case n = 2. There are 18 possible cases. We present by generators and relations the corresponding Nichols algebras on five of these eighteen cases. As an application, we characterize finite-dimensional Nichols algebras over indecomposable modules for n = 2 = m and n = 2, m = 3, which recovers some results of the second and third author in the former case, and of Xiong in the latter.Fil: Bagio, D.. Universidade Federal de Santa Maria; BrasilFil: García, Gastón Andrés. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata; ArgentinaFil: Jury Giraldi, Joao Matheus. Universidade Federal de Santa Maria; BrasilFil: Márquez, O.. Universidade Federal de Santa Maria; BrasilWorld Scientific2021-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/150434Bagio, D.; García, Gastón Andrés; Jury Giraldi, Joao Matheus; Márquez, O.; Finite-dimensional Nichols algebras over dual Radford algebras; World Scientific; Journal of Algebra and its Applications; 20; 1; 1-2021; 1-290219-49881793-6829CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://www.worldscientific.com/doi/10.1142/S0219498821400016info:eu-repo/semantics/altIdentifier/doi/10.1142/S0219498821400016info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1910.05408info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T10:02:20Zoai:ri.conicet.gov.ar:11336/150434instacron: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 10:02:20.44CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Finite-dimensional Nichols algebras over dual Radford algebras
title Finite-dimensional Nichols algebras over dual Radford algebras
spellingShingle Finite-dimensional Nichols algebras over dual Radford algebras
Bagio, D.
DUAL RADFORD HOPF ALGEBRA
HOPF ALGEBRA
NICHOLS ALGEBRA
STANDARD FILTRATION
title_short Finite-dimensional Nichols algebras over dual Radford algebras
title_full Finite-dimensional Nichols algebras over dual Radford algebras
title_fullStr Finite-dimensional Nichols algebras over dual Radford algebras
title_full_unstemmed Finite-dimensional Nichols algebras over dual Radford algebras
title_sort Finite-dimensional Nichols algebras over dual Radford algebras
dc.creator.none.fl_str_mv Bagio, D.
García, Gastón Andrés
Jury Giraldi, Joao Matheus
Márquez, O.
author Bagio, D.
author_facet Bagio, D.
García, Gastón Andrés
Jury Giraldi, Joao Matheus
Márquez, O.
author_role author
author2 García, Gastón Andrés
Jury Giraldi, Joao Matheus
Márquez, O.
author2_role author
author
author
dc.subject.none.fl_str_mv DUAL RADFORD HOPF ALGEBRA
HOPF ALGEBRA
NICHOLS ALGEBRA
STANDARD FILTRATION
topic DUAL RADFORD HOPF ALGEBRA
HOPF ALGEBRA
NICHOLS ALGEBRA
STANDARD FILTRATION
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv For n, m ∈ N, let Hn,m be the dual of the Radford algebra of dimension n 2m. We present new finite-dimensional Nichols algebras arising from the study of simple Yetter-Drinfeld modules over Hn,m. Along the way, we describe the simple objects in Hn,m Hn,m YD and their projective envelopes. Then, we determine those simple modules that give rise to finite-dimensional Nichols algebras for the case n = 2. There are 18 possible cases. We present by generators and relations the corresponding Nichols algebras on five of these eighteen cases. As an application, we characterize finite-dimensional Nichols algebras over indecomposable modules for n = 2 = m and n = 2, m = 3, which recovers some results of the second and third author in the former case, and of Xiong in the latter.
Fil: Bagio, D.. Universidade Federal de Santa Maria; Brasil
Fil: García, Gastón Andrés. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata; Argentina
Fil: Jury Giraldi, Joao Matheus. Universidade Federal de Santa Maria; Brasil
Fil: Márquez, O.. Universidade Federal de Santa Maria; Brasil
description For n, m ∈ N, let Hn,m be the dual of the Radford algebra of dimension n 2m. We present new finite-dimensional Nichols algebras arising from the study of simple Yetter-Drinfeld modules over Hn,m. Along the way, we describe the simple objects in Hn,m Hn,m YD and their projective envelopes. Then, we determine those simple modules that give rise to finite-dimensional Nichols algebras for the case n = 2. There are 18 possible cases. We present by generators and relations the corresponding Nichols algebras on five of these eighteen cases. As an application, we characterize finite-dimensional Nichols algebras over indecomposable modules for n = 2 = m and n = 2, m = 3, which recovers some results of the second and third author in the former case, and of Xiong in the latter.
publishDate 2021
dc.date.none.fl_str_mv 2021-01
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/11336/150434
Bagio, D.; García, Gastón Andrés; Jury Giraldi, Joao Matheus; Márquez, O.; Finite-dimensional Nichols algebras over dual Radford algebras; World Scientific; Journal of Algebra and its Applications; 20; 1; 1-2021; 1-29
0219-4988
1793-6829
CONICET Digital
CONICET
url http://hdl.handle.net/11336/150434
identifier_str_mv Bagio, D.; García, Gastón Andrés; Jury Giraldi, Joao Matheus; Márquez, O.; Finite-dimensional Nichols algebras over dual Radford algebras; World Scientific; Journal of Algebra and its Applications; 20; 1; 1-2021; 1-29
0219-4988
1793-6829
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://www.worldscientific.com/doi/10.1142/S0219498821400016
info:eu-repo/semantics/altIdentifier/doi/10.1142/S0219498821400016
info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1910.05408
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
application/pdf
application/pdf
dc.publisher.none.fl_str_mv World Scientific
publisher.none.fl_str_mv World Scientific
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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