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
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/8987
Ver los metadatos del registro completo
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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 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/11336/8987 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 |
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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/ |
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