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dc.contributor.author
Beattie, Margaret
dc.contributor.author
García, Gastón Andrés
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dc.date.available
2016-12-07T16:26:48Z
dc.date.issued
2013-01
dc.identifier.citation
Beattie, Margaret ; García, Gastón Andrés; Classifying Hopf algebras of a given dimension; Contemporary Mathematics; 585; 1-2013; 125-152
dc.identifier.issn
0271-4132
dc.identifier.uri
http://hdl.handle.net/11336/8987
dc.description.abstract
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.
dc.format
application/pdf
dc.language.iso
eng
dc.rights
info:eu-repo/semantics/openAccess
dc.rights.uri
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.subject
Finite Dimensional Hopf Algebras
dc.subject
Classification
dc.subject.classification
Matemática Pura
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dc.subject.classification
Matemáticas
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dc.subject.classification
CIENCIAS NATURALES Y EXACTAS
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dc.title
Classifying Hopf algebras of a given dimension
dc.type
info:eu-repo/semantics/article
dc.type
info:ar-repo/semantics/artículo
dc.type
info:eu-repo/semantics/publishedVersion
dc.date.updated
2016-11-25T14:01:11Z
dc.journal.volume
585
dc.journal.pagination
125-152
dc.journal.pais
Estados Unidos
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dc.conicet.avisoEditorial
First published in Contemporary Mathematics in 585, 2013, published by the American Mathematical Society
dc.description.fil
Fil: Beattie, Margaret . Mount Allison Faculty; Estados Unidos
dc.description.fil
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
dc.journal.title
Contemporary Mathematics
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dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1206.6529v2
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/doi/http://dx.doi.org/10.1090/conm/585/11615
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/url/http://www.ams.org/books/conm/585/
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