On finite-dimensional copointed Hopf algebras over dihedral groups

Autores
Fantino, Fernando Amado; García, Gastón Andrés; Mastnak, Mitja
Año de publicación
2019
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We classify all finite-dimensional Hopf algebras over an algebraically closed field of characteristic zero such that its coradical is isomorphic to the algebra of functions k D m over a dihedral group D m , with m=4a≥12. We obtain this classification by means of the lifting method, where we use cohomology theory to determine all possible deformations. Our result provides an infinite family of new examples of finite-dimensional copointed Hopf algebras over dihedral groups.
Fil: Fantino, Fernando Amado. 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: 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: Mastnak, Mitja. Saint Mary's University; Canadá
Materia
DEFORMATIONS
DIHEDRAL GROUP
HOPF ALGEBRAS
NICHOLS ALGEBRAS
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/83342
Acceder
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network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling On finite-dimensional copointed Hopf algebras over dihedral groupsFantino, Fernando AmadoGarcía, Gastón AndrésMastnak, MitjaDEFORMATIONSDIHEDRAL GROUPHOPF ALGEBRASNICHOLS ALGEBRAShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We classify all finite-dimensional Hopf algebras over an algebraically closed field of characteristic zero such that its coradical is isomorphic to the algebra of functions k D m over a dihedral group D m , with m=4a≥12. We obtain this classification by means of the lifting method, where we use cohomology theory to determine all possible deformations. Our result provides an infinite family of new examples of finite-dimensional copointed Hopf algebras over dihedral groups.Fil: Fantino, Fernando Amado. 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: 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: Mastnak, Mitja. Saint Mary's University; CanadáElsevier Science2019-08info: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/11336/83342Fantino, Fernando Amado; García, Gastón Andrés; Mastnak, Mitja; On finite-dimensional copointed Hopf algebras over dihedral groups; Elsevier Science; Journal Of Pure And Applied Algebra; 223; 8; 8-2019; 3611-36340022-4049CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0022404918302895info:eu-repo/semantics/altIdentifier/doi/10.1016/j.jpaa.2018.11.021info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1608.06167info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-nd/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T10:04:55Zoai:ri.conicet.gov.ar:11336/83342instacron: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 10:04:56.185CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv On finite-dimensional copointed Hopf algebras over dihedral groups
title On finite-dimensional copointed Hopf algebras over dihedral groups
spellingShingle On finite-dimensional copointed Hopf algebras over dihedral groups
Fantino, Fernando Amado
DEFORMATIONS
DIHEDRAL GROUP
HOPF ALGEBRAS
NICHOLS ALGEBRAS
title_short On finite-dimensional copointed Hopf algebras over dihedral groups
title_full On finite-dimensional copointed Hopf algebras over dihedral groups
title_fullStr On finite-dimensional copointed Hopf algebras over dihedral groups
title_full_unstemmed On finite-dimensional copointed Hopf algebras over dihedral groups
title_sort On finite-dimensional copointed Hopf algebras over dihedral groups
dc.creator.none.fl_str_mv Fantino, Fernando Amado
García, Gastón Andrés
Mastnak, Mitja
author Fantino, Fernando Amado
author_facet Fantino, Fernando Amado
García, Gastón Andrés
Mastnak, Mitja
author_role author
author2 García, Gastón Andrés
Mastnak, Mitja
author2_role author
author
dc.subject.none.fl_str_mv DEFORMATIONS
DIHEDRAL GROUP
HOPF ALGEBRAS
NICHOLS ALGEBRAS
topic DEFORMATIONS
DIHEDRAL GROUP
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 classify all finite-dimensional Hopf algebras over an algebraically closed field of characteristic zero such that its coradical is isomorphic to the algebra of functions k D m over a dihedral group D m , with m=4a≥12. We obtain this classification by means of the lifting method, where we use cohomology theory to determine all possible deformations. Our result provides an infinite family of new examples of finite-dimensional copointed Hopf algebras over dihedral groups.
Fil: Fantino, Fernando Amado. 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: 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: Mastnak, Mitja. Saint Mary's University; Canadá
description We classify all finite-dimensional Hopf algebras over an algebraically closed field of characteristic zero such that its coradical is isomorphic to the algebra of functions k D m over a dihedral group D m , with m=4a≥12. We obtain this classification by means of the lifting method, where we use cohomology theory to determine all possible deformations. Our result provides an infinite family of new examples of finite-dimensional copointed Hopf algebras over dihedral groups.
publishDate 2019
dc.date.none.fl_str_mv 2019-08
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/11336/83342
Fantino, Fernando Amado; García, Gastón Andrés; Mastnak, Mitja; On finite-dimensional copointed Hopf algebras over dihedral groups; Elsevier Science; Journal Of Pure And Applied Algebra; 223; 8; 8-2019; 3611-3634
0022-4049
CONICET Digital
CONICET
url http://hdl.handle.net/11336/83342
identifier_str_mv Fantino, Fernando Amado; García, Gastón Andrés; Mastnak, Mitja; On finite-dimensional copointed Hopf algebras over dihedral groups; Elsevier Science; Journal Of Pure And Applied Algebra; 223; 8; 8-2019; 3611-3634
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/url/https://www.sciencedirect.com/science/article/pii/S0022404918302895
info:eu-repo/semantics/altIdentifier/doi/10.1016/j.jpaa.2018.11.021
info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1608.06167
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
dc.format.none.fl_str_mv application/pdf
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 13.13397

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