On a family of Hopf algebras of dimension 72

Autores
Andruskiewitsch, Nicolas; Vay, Cristian Damian
Año de publicación
2012
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We investigate a family of Hopf algebras of dimension 72 whose coradical is isomorphic to the algebra of functions on S3. We determine the lattice of submodules of the so-called Verma modules and as a consequence we classify all simple modules. We show that these Hopf algebras are unimodular (as well as their duals) but not quasitriangular; also, they are cocycle deformations of each other.
Fil: Andruskiewitsch, Nicolas. 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
Fil: Vay, Cristian Damian. 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
Materia
Hopf algebras
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:11336/199291
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/199291
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network_name_str CONICET Digital (CONICET)
spelling On a family of Hopf algebras of dimension 72Andruskiewitsch, NicolasVay, Cristian DamianHopf algebrashttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We investigate a family of Hopf algebras of dimension 72 whose coradical is isomorphic to the algebra of functions on S3. We determine the lattice of submodules of the so-called Verma modules and as a consequence we classify all simple modules. We show that these Hopf algebras are unimodular (as well as their duals) but not quasitriangular; also, they are cocycle deformations of each other.Fil: Andruskiewitsch, Nicolas. 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; ArgentinaFil: Vay, Cristian Damian. 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; ArgentinaBelgian Mathematical Soc Triomphe2012-06info: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/11336/199291Andruskiewitsch, Nicolas; Vay, Cristian Damian; On a family of Hopf algebras of dimension 72; Belgian Mathematical Soc Triomphe; Bulletin Of The Belgian Mathematical Society-simon Stevin; 19; 6-2012; 415-4431370-1444CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/arxiv/https://arxiv.org/abs/1105.0394info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T09:58:39Zoai:ri.conicet.gov.ar:11336/199291instacron: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 09:58:39.657CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv On a family of Hopf algebras of dimension 72
title On a family of Hopf algebras of dimension 72
spellingShingle On a family of Hopf algebras of dimension 72
Andruskiewitsch, Nicolas
Hopf algebras
title_short On a family of Hopf algebras of dimension 72
title_full On a family of Hopf algebras of dimension 72
title_fullStr On a family of Hopf algebras of dimension 72
title_full_unstemmed On a family of Hopf algebras of dimension 72
title_sort On a family of Hopf algebras of dimension 72
dc.creator.none.fl_str_mv Andruskiewitsch, Nicolas
Vay, Cristian Damian
author Andruskiewitsch, Nicolas
author_facet Andruskiewitsch, Nicolas
Vay, Cristian Damian
author_role author
author2 Vay, Cristian Damian
author2_role author
dc.subject.none.fl_str_mv Hopf algebras
topic Hopf 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 investigate a family of Hopf algebras of dimension 72 whose coradical is isomorphic to the algebra of functions on S3. We determine the lattice of submodules of the so-called Verma modules and as a consequence we classify all simple modules. We show that these Hopf algebras are unimodular (as well as their duals) but not quasitriangular; also, they are cocycle deformations of each other.
Fil: Andruskiewitsch, Nicolas. 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
Fil: Vay, Cristian Damian. 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
description We investigate a family of Hopf algebras of dimension 72 whose coradical is isomorphic to the algebra of functions on S3. We determine the lattice of submodules of the so-called Verma modules and as a consequence we classify all simple modules. We show that these Hopf algebras are unimodular (as well as their duals) but not quasitriangular; also, they are cocycle deformations of each other.
publishDate 2012
dc.date.none.fl_str_mv 2012-06
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/11336/199291
Andruskiewitsch, Nicolas; Vay, Cristian Damian; On a family of Hopf algebras of dimension 72; Belgian Mathematical Soc Triomphe; Bulletin Of The Belgian Mathematical Society-simon Stevin; 19; 6-2012; 415-443
1370-1444
CONICET Digital
CONICET
url http://hdl.handle.net/11336/199291
identifier_str_mv Andruskiewitsch, Nicolas; Vay, Cristian Damian; On a family of Hopf algebras of dimension 72; Belgian Mathematical Soc Triomphe; Bulletin Of The Belgian Mathematical Society-simon Stevin; 19; 6-2012; 415-443
1370-1444
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/arxiv/https://arxiv.org/abs/1105.0394
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 Belgian Mathematical Soc Triomphe
publisher.none.fl_str_mv Belgian Mathematical Soc Triomphe
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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