Deformation by cocycles of pointed Hopf algebras over non-abelian groups

We explore a method for explicitly constructing multiplicative 2-cocycles for bosonizations of Nichols algebras B(V ) over Hopf algebras H. These cocycles arise as liftings of H-invariant linear functionals on V⊗ V and give a formula for deforming braidedcommutator- Type relations. Using this constr...

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Detalles Bibliográficos
Autores: García, Gastón Andrés, Mastnak, Mitja
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:11336/49868
Acceso en línea:http://hdl.handle.net/11336/49868
Access Level:acceso abierto
Palabra clave:Hopf Algebras
Dihedral Groups
2-Cocycles
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
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spelling Deformation by cocycles of pointed Hopf algebras over non-abelian groupsGarcía, Gastón AndrésMastnak, MitjaHopf AlgebrasDihedral Groups2-Cocycleshttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We explore a method for explicitly constructing multiplicative 2-cocycles for bosonizations of Nichols algebras B(V ) over Hopf algebras H. These cocycles arise as liftings of H-invariant linear functionals on V⊗ V and give a formula for deforming braidedcommutator- Type relations. Using this construction, we show that all known finite-dimensional pointed Hopf algebras over the dihedral groups Dm with m = 4t≥12, over the symmetric group S3, and some families over S4 are cocycle deformations of bosonizations of Nichols algebras.Fil: García, Gastón Andrés. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; ArgentinaFil: Mastnak, Mitja. Saint Mary’s University; CanadáInternational Press Boston2015-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/49868García, Gastón Andrés; Mastnak, Mitja; Deformation by cocycles of pointed Hopf algebras over non-abelian groups; International Press Boston; Mathematical Research Letters; 22; 1; 1-2015; 59-921073-2780CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.4310/MRL.2015.v22.n1.a5info:eu-repo/semantics/altIdentifier/url/http://www.intlpress.com/site/pub/pages/journals/items/mrl/content/vols/0022/0001/a005/info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2024-05-08T13:44:29Zoai:ri.conicet.gov.ar:11336/49868instacron: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 13:44:29.354CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Deformation by cocycles of pointed Hopf algebras over non-abelian groups
title Deformation by cocycles of pointed Hopf algebras over non-abelian groups
spellingShingle Deformation by cocycles of pointed Hopf algebras over non-abelian groups
García, Gastón Andrés
Hopf Algebras
Dihedral Groups
2-Cocycles
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
title_short Deformation by cocycles of pointed Hopf algebras over non-abelian groups
title_full Deformation by cocycles of pointed Hopf algebras over non-abelian groups
title_fullStr Deformation by cocycles of pointed Hopf algebras over non-abelian groups
title_full_unstemmed Deformation by cocycles of pointed Hopf algebras over non-abelian groups
title_sort Deformation by cocycles of pointed Hopf algebras over non-abelian groups
dc.creator.none.fl_str_mv García, Gastón Andrés
Mastnak, Mitja
author García, Gastón Andrés
author_facet García, Gastón Andrés
Mastnak, Mitja
author_role author
author2 Mastnak, Mitja
author2_role author
dc.subject.none.fl_str_mv Hopf Algebras
Dihedral Groups
2-Cocycles
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
topic Hopf Algebras
Dihedral Groups
2-Cocycles
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
description We explore a method for explicitly constructing multiplicative 2-cocycles for bosonizations of Nichols algebras B(V ) over Hopf algebras H. These cocycles arise as liftings of H-invariant linear functionals on V⊗ V and give a formula for deforming braidedcommutator- Type relations. Using this construction, we show that all known finite-dimensional pointed Hopf algebras over the dihedral groups Dm with m = 4t≥12, over the symmetric group S3, and some families over S4 are cocycle deformations of bosonizations of Nichols algebras.
publishDate 2015
dc.date.none.fl_str_mv 2015-01
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/11336/49868
García, Gastón Andrés; Mastnak, Mitja; Deformation by cocycles of pointed Hopf algebras over non-abelian groups; International Press Boston; Mathematical Research Letters; 22; 1; 1-2015; 59-92
1073-2780
CONICET Digital
CONICET
url http://hdl.handle.net/11336/49868
identifier_str_mv García, Gastón Andrés; Mastnak, Mitja; Deformation by cocycles of pointed Hopf algebras over non-abelian groups; International Press Boston; Mathematical Research Letters; 22; 1; 1-2015; 59-92
1073-2780
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.4310/MRL.2015.v22.n1.a5
info:eu-repo/semantics/altIdentifier/url/http://www.intlpress.com/site/pub/pages/journals/items/mrl/content/vols/0022/0001/a005/
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
dc.publisher.none.fl_str_mv International Press Boston
publisher.none.fl_str_mv International Press Boston
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 15,811543

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