Deformation by cocycles of pointed Hopf algebras over non-abelian groups
- Autores
- García, Gastón Andrés; Mastnak, Mitja
- Año de publicación
- 2015
- Idioma
- inglés
- Tipo de recurso
- artículo
- Estado
- versión publicada
- Descripción
- 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.
Fil: García, Gastón Andrés. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; Argentina
Fil: Mastnak, Mitja. Saint Mary’s University; Canadá - Materia
-
Hopf Algebras
Dihedral Groups
2-Cocycles - Nivel de accesibilidad
- acceso abierto
- Condiciones de uso
- https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
- Repositorio
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/49868
Ver los metadatos del registro completo
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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 Técnicas2025-09-29T09:47:44Zoai: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:34982025-09-29 09:47:44.551CONICET 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 |
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 |
topic |
Hopf Algebras Dihedral Groups 2-Cocycles |
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 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; Argentina Fil: Mastnak, Mitja. Saint Mary’s University; Canadá |
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 |
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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1844613486227750912 |
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13.070432 |