Techniques for classifying Hopf algebras and applications to dimension p3

Autores
Beattie, M.; García, Gastón Andrés
Año de publicación
2013
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Classifying Hopf algebras of a given finite dimension n over C is a challenging problem. If n is p, p^2, 2p, or 2p^2 with p prime, the classification is complete. If n = p^3, the semisimple and the pointed Hopf algebras are classified and much progress on the remaining cases was made by the second author but the general classification is still open. Here we outline some results and techniques which have been useful in approaching this problem and add a few new ones. We give some further results on Hopf algebras of dimension p^3 and finish the classification for dimension 27.
Fil: Beattie, M.. Mount Allison University; Canadá
Fil: García, Gastón Andrés. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Córdoba. Centro de Investigación y Estudios de Matemática de Córdoba(p); Argentina
Materia
Hopf Algebras of Small Dimension
Pointed
Copointed
Chevalley Property
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:11336/8931
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/8931
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Techniques for classifying Hopf algebras and applications to dimension p3Beattie, M.García, Gastón AndrésHopf Algebras of Small DimensionPointedCopointedChevalley Propertyhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Classifying Hopf algebras of a given finite dimension n over C is a challenging problem. If n is p, p^2, 2p, or 2p^2 with p prime, the classification is complete. If n = p^3, the semisimple and the pointed Hopf algebras are classified and much progress on the remaining cases was made by the second author but the general classification is still open. Here we outline some results and techniques which have been useful in approaching this problem and add a few new ones. We give some further results on Hopf algebras of dimension p^3 and finish the classification for dimension 27.Fil: Beattie, M.. Mount Allison University; CanadáFil: García, Gastón Andrés. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Córdoba. Centro de Investigación y Estudios de Matemática de Córdoba(p); ArgentinaTaylor & Francis2013-06info: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/11336/8931Beattie, M.; García, Gastón Andrés; Techniques for classifying Hopf algebras and applications to dimension p3; Taylor & Francis; Communications In Algebra; 41; 8; 6-2013; 3108-31290092-7872enginfo:eu-repo/semantics/altIdentifier/doi/10.1080/00927872.2012.692004info:eu-repo/semantics/altIdentifier/url/http://www.tandfonline.com/doi/abs/10.1080/00927872.2012.692004info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T10:29:26Zoai:ri.conicet.gov.ar:11336/8931instacron: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 10:29:27.045CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Techniques for classifying Hopf algebras and applications to dimension p3
title Techniques for classifying Hopf algebras and applications to dimension p3
spellingShingle Techniques for classifying Hopf algebras and applications to dimension p3
Beattie, M.
Hopf Algebras of Small Dimension
Pointed
Copointed
Chevalley Property
title_short Techniques for classifying Hopf algebras and applications to dimension p3
title_full Techniques for classifying Hopf algebras and applications to dimension p3
title_fullStr Techniques for classifying Hopf algebras and applications to dimension p3
title_full_unstemmed Techniques for classifying Hopf algebras and applications to dimension p3
title_sort Techniques for classifying Hopf algebras and applications to dimension p3
dc.creator.none.fl_str_mv Beattie, M.
García, Gastón Andrés
author Beattie, M.
author_facet Beattie, M.
García, Gastón Andrés
author_role author
author2 García, Gastón Andrés
author2_role author
dc.subject.none.fl_str_mv Hopf Algebras of Small Dimension
Pointed
Copointed
Chevalley Property
topic Hopf Algebras of Small Dimension
Pointed
Copointed
Chevalley Property
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv Classifying Hopf algebras of a given finite dimension n over C is a challenging problem. If n is p, p^2, 2p, or 2p^2 with p prime, the classification is complete. If n = p^3, the semisimple and the pointed Hopf algebras are classified and much progress on the remaining cases was made by the second author but the general classification is still open. Here we outline some results and techniques which have been useful in approaching this problem and add a few new ones. We give some further results on Hopf algebras of dimension p^3 and finish the classification for dimension 27.
Fil: Beattie, M.. Mount Allison University; Canadá
Fil: García, Gastón Andrés. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Córdoba. Centro de Investigación y Estudios de Matemática de Córdoba(p); Argentina
description Classifying Hopf algebras of a given finite dimension n over C is a challenging problem. If n is p, p^2, 2p, or 2p^2 with p prime, the classification is complete. If n = p^3, the semisimple and the pointed Hopf algebras are classified and much progress on the remaining cases was made by the second author but the general classification is still open. Here we outline some results and techniques which have been useful in approaching this problem and add a few new ones. We give some further results on Hopf algebras of dimension p^3 and finish the classification for dimension 27.
publishDate 2013
dc.date.none.fl_str_mv 2013-06
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/11336/8931
Beattie, M.; García, Gastón Andrés; Techniques for classifying Hopf algebras and applications to dimension p3; Taylor & Francis; Communications In Algebra; 41; 8; 6-2013; 3108-3129
0092-7872
url http://hdl.handle.net/11336/8931
identifier_str_mv Beattie, M.; García, Gastón Andrés; Techniques for classifying Hopf algebras and applications to dimension p3; Taylor & Francis; Communications In Algebra; 41; 8; 6-2013; 3108-3129
0092-7872
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1080/00927872.2012.692004
info:eu-repo/semantics/altIdentifier/url/http://www.tandfonline.com/doi/abs/10.1080/00927872.2012.692004
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 Taylor & Francis
publisher.none.fl_str_mv Taylor & Francis
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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