Classifying Hopf algebras of a given dimension

Autores
Beattie, Margaret; García, Gastón Andrés
Año de publicación
2013
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Classifying all Hopf algebras of a given finite dimension over C is a challenging problem which remains open even for many small dimensions, not least because few general approaches to the problem are known. Some useful techniques include counting the dimensions of spaces related to the coradical filtration in D. Fukuda (Glasg. 2008), N. Andruskiewitsch and S. Natale (2001), M. Beattie and S. D¢asc¢alescu (2004), studying sub- and quotient Hopf algebras in G.A. Garcia (2005), G.A. Garcia and C. Vay (2010), especially those sub-Hopf algebras generated by a simple subcoalgebra in S. Natale (2002), working with the antipode in S-H. Ng (2002), (2004), (2005), (2008), and studying Hopf algebras in Yetter-Drinfeld categories to help to classify Radford biproducts in Y-l. Cheng and S-H. Ng (2011). In this paper, we add to the classification tools in M. Beattie and G.A. Garcia (to appear) and apply our results to Hopf algebras of dimension rpq and 8p where p, q, r are distinct primes. At the end of this paper we summarize in a table the status of the classification for dimensions up to 100 to date.
Fil: Beattie, Margaret . Mount Allison Faculty; Estados Unidos
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
FINITE DIMENSIONAL HOPF ALGEBRAS
CLASSIFICATION
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:11336/8987

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spelling Classifying Hopf algebras of a given dimensionBeattie, Margaret García, Gastón AndrésFINITE DIMENSIONAL HOPF ALGEBRASCLASSIFICATIONhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Classifying all Hopf algebras of a given finite dimension over C is a challenging problem which remains open even for many small dimensions, not least because few general approaches to the problem are known. Some useful techniques include counting the dimensions of spaces related to the coradical filtration in D. Fukuda (Glasg. 2008), N. Andruskiewitsch and S. Natale (2001), M. Beattie and S. D¢asc¢alescu (2004), studying sub- and quotient Hopf algebras in G.A. Garcia (2005), G.A. Garcia and C. Vay (2010), especially those sub-Hopf algebras generated by a simple subcoalgebra in S. Natale (2002), working with the antipode in S-H. Ng (2002), (2004), (2005), (2008), and studying Hopf algebras in Yetter-Drinfeld categories to help to classify Radford biproducts in Y-l. Cheng and S-H. Ng (2011). In this paper, we add to the classification tools in M. Beattie and G.A. Garcia (to appear) and apply our results to Hopf algebras of dimension rpq and 8p where p, q, r are distinct primes. At the end of this paper we summarize in a table the status of the classification for dimensions up to 100 to date.Fil: Beattie, Margaret . Mount Allison Faculty; Estados UnidosFil: 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); Argentina2013-01info: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/11336/8987Beattie, Margaret ; García, Gastón Andrés; Classifying Hopf algebras of a given dimension; Contemporary Mathematics; 585; 1-2013; 125-1520271-4132enginfo:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1206.6529v2info:eu-repo/semantics/altIdentifier/doi/10.1090/conm/585/11615info:eu-repo/semantics/altIdentifier/url/http://www.ams.org/books/conm/585/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 Técnicas2025-09-29T10:10:10Zoai:ri.conicet.gov.ar:11336/8987instacron: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 10:10:10.996CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Classifying Hopf algebras of a given dimension
title Classifying Hopf algebras of a given dimension
spellingShingle Classifying Hopf algebras of a given dimension
Beattie, Margaret
FINITE DIMENSIONAL HOPF ALGEBRAS
CLASSIFICATION
title_short Classifying Hopf algebras of a given dimension
title_full Classifying Hopf algebras of a given dimension
title_fullStr Classifying Hopf algebras of a given dimension
title_full_unstemmed Classifying Hopf algebras of a given dimension
title_sort Classifying Hopf algebras of a given dimension
dc.creator.none.fl_str_mv Beattie, Margaret
García, Gastón Andrés
author Beattie, Margaret
author_facet Beattie, Margaret
García, Gastón Andrés
author_role author
author2 García, Gastón Andrés
author2_role author
dc.subject.none.fl_str_mv FINITE DIMENSIONAL HOPF ALGEBRAS
CLASSIFICATION
topic FINITE DIMENSIONAL HOPF ALGEBRAS
CLASSIFICATION
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 all Hopf algebras of a given finite dimension over C is a challenging problem which remains open even for many small dimensions, not least because few general approaches to the problem are known. Some useful techniques include counting the dimensions of spaces related to the coradical filtration in D. Fukuda (Glasg. 2008), N. Andruskiewitsch and S. Natale (2001), M. Beattie and S. D¢asc¢alescu (2004), studying sub- and quotient Hopf algebras in G.A. Garcia (2005), G.A. Garcia and C. Vay (2010), especially those sub-Hopf algebras generated by a simple subcoalgebra in S. Natale (2002), working with the antipode in S-H. Ng (2002), (2004), (2005), (2008), and studying Hopf algebras in Yetter-Drinfeld categories to help to classify Radford biproducts in Y-l. Cheng and S-H. Ng (2011). In this paper, we add to the classification tools in M. Beattie and G.A. Garcia (to appear) and apply our results to Hopf algebras of dimension rpq and 8p where p, q, r are distinct primes. At the end of this paper we summarize in a table the status of the classification for dimensions up to 100 to date.
Fil: Beattie, Margaret . Mount Allison Faculty; Estados Unidos
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 all Hopf algebras of a given finite dimension over C is a challenging problem which remains open even for many small dimensions, not least because few general approaches to the problem are known. Some useful techniques include counting the dimensions of spaces related to the coradical filtration in D. Fukuda (Glasg. 2008), N. Andruskiewitsch and S. Natale (2001), M. Beattie and S. D¢asc¢alescu (2004), studying sub- and quotient Hopf algebras in G.A. Garcia (2005), G.A. Garcia and C. Vay (2010), especially those sub-Hopf algebras generated by a simple subcoalgebra in S. Natale (2002), working with the antipode in S-H. Ng (2002), (2004), (2005), (2008), and studying Hopf algebras in Yetter-Drinfeld categories to help to classify Radford biproducts in Y-l. Cheng and S-H. Ng (2011). In this paper, we add to the classification tools in M. Beattie and G.A. Garcia (to appear) and apply our results to Hopf algebras of dimension rpq and 8p where p, q, r are distinct primes. At the end of this paper we summarize in a table the status of the classification for dimensions up to 100 to date.
publishDate 2013
dc.date.none.fl_str_mv 2013-01
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
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info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/8987
Beattie, Margaret ; García, Gastón Andrés; Classifying Hopf algebras of a given dimension; Contemporary Mathematics; 585; 1-2013; 125-152
0271-4132
url http://hdl.handle.net/11336/8987
identifier_str_mv Beattie, Margaret ; García, Gastón Andrés; Classifying Hopf algebras of a given dimension; Contemporary Mathematics; 585; 1-2013; 125-152
0271-4132
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1206.6529v2
info:eu-repo/semantics/altIdentifier/doi/10.1090/conm/585/11615
info:eu-repo/semantics/altIdentifier/url/http://www.ams.org/books/conm/585/
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
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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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