On rigidity of Nichols algebras

Autores
Angiono, Iván Ezequiel; Kochetov, Mikhail; Mastnak, Mitja
Año de publicación
2015
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We study deformations of graded braided bialgebras using cohomological methods. In particular, we show that many examples of Nichols algebras, including the finite-dimensional ones arising in the Andruskiewitsch-Schneider program of classification of pointed Hopf algebras, are rigid. This result can be regarded as nonexistence of "braided Lie algebras" with nontrivial bracket.
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; Argentina. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina
Fil: Kochetov, Mikhail. Memorial University Of Newfoundland; Canadá
Fil: Mastnak, Mitja. School Of Environmental Studies. Saint Mary's University; Canadá
Materia
Hopf Algebras
Braided Tensor Categories
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:11336/51323
Acceder
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network_name_str CONICET Digital (CONICET)
spelling On rigidity of Nichols algebrasAngiono, Iván EzequielKochetov, MikhailMastnak, MitjaHopf AlgebrasBraided Tensor Categorieshttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We study deformations of graded braided bialgebras using cohomological methods. In particular, we show that many examples of Nichols algebras, including the finite-dimensional ones arising in the Andruskiewitsch-Schneider program of classification of pointed Hopf algebras, are rigid. This result can be regarded as nonexistence of "braided Lie algebras" with nontrivial bracket.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; Argentina. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; ArgentinaFil: Kochetov, Mikhail. Memorial University Of Newfoundland; CanadáFil: Mastnak, Mitja. School Of Environmental Studies. Saint Mary's University; CanadáElsevier Science2015-12info: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/11336/51323Angiono, Iván Ezequiel; Kochetov, Mikhail; Mastnak, Mitja; On rigidity of Nichols algebras; Elsevier Science; Journal Of Pure And Applied Algebra; 219; 12; 12-2015; 5539-55590022-4049CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1016/j.jpaa.2015.05.032info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0022404915001474info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-11-12T09:35:38Zoai:ri.conicet.gov.ar:11336/51323instacron: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:34982025-11-12 09:35:38.546CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv On rigidity of Nichols algebras
title On rigidity of Nichols algebras
spellingShingle On rigidity of Nichols algebras
Angiono, Iván Ezequiel
Hopf Algebras
Braided Tensor Categories
title_short On rigidity of Nichols algebras
title_full On rigidity of Nichols algebras
title_fullStr On rigidity of Nichols algebras
title_full_unstemmed On rigidity of Nichols algebras
title_sort On rigidity of Nichols algebras
dc.creator.none.fl_str_mv Angiono, Iván Ezequiel
Kochetov, Mikhail
Mastnak, Mitja
author Angiono, Iván Ezequiel
author_facet Angiono, Iván Ezequiel
Kochetov, Mikhail
Mastnak, Mitja
author_role author
author2 Kochetov, Mikhail
Mastnak, Mitja
author2_role author
author
dc.subject.none.fl_str_mv Hopf Algebras
Braided Tensor Categories
topic Hopf Algebras
Braided Tensor Categories
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 study deformations of graded braided bialgebras using cohomological methods. In particular, we show that many examples of Nichols algebras, including the finite-dimensional ones arising in the Andruskiewitsch-Schneider program of classification of pointed Hopf algebras, are rigid. This result can be regarded as nonexistence of "braided Lie algebras" with nontrivial bracket.
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; Argentina. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina
Fil: Kochetov, Mikhail. Memorial University Of Newfoundland; Canadá
Fil: Mastnak, Mitja. School Of Environmental Studies. Saint Mary's University; Canadá
description We study deformations of graded braided bialgebras using cohomological methods. In particular, we show that many examples of Nichols algebras, including the finite-dimensional ones arising in the Andruskiewitsch-Schneider program of classification of pointed Hopf algebras, are rigid. This result can be regarded as nonexistence of "braided Lie algebras" with nontrivial bracket.
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/11336/51323
Angiono, Iván Ezequiel; Kochetov, Mikhail; Mastnak, Mitja; On rigidity of Nichols algebras; Elsevier Science; Journal Of Pure And Applied Algebra; 219; 12; 12-2015; 5539-5559
0022-4049
CONICET Digital
CONICET
url http://hdl.handle.net/11336/51323
identifier_str_mv Angiono, Iván Ezequiel; Kochetov, Mikhail; Mastnak, Mitja; On rigidity of Nichols algebras; Elsevier Science; Journal Of Pure And Applied Algebra; 219; 12; 12-2015; 5539-5559
0022-4049
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1016/j.jpaa.2015.05.032
info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0022404915001474
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
dc.publisher.none.fl_str_mv Elsevier Science
publisher.none.fl_str_mv Elsevier Science
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 12.976206

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