From racks to pointed Hopf algebras

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A fundamental step in the classification of finite-dimensional complex pointed Hopf algebras is the determination of all finite-dimensional Nichols algebras of braided vector spaces arising from groups. The most important class of braided vector spaces arising from groups is the class of braided vec...

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Autores principales: Andruskiewitsch, N., Graña, M.
Formato: Artículo publishedVersion
Publicado: 2003
Materias:
Pointed Hopf algebras
Quandles
Racks
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_00018708_v178_n2_p177_Andruskiewitsch
https://repositoriouba.sisbi.uba.ar/gsdl/cgi-bin/library.cgi?a=d&c=artiaex&d=paper_00018708_v178_n2_p177_Andruskiewitsch_oai
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id I28-R145-paper_00018708_v178_n2_p177_Andruskiewitsch_oai
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spelling I28-R145-paper_00018708_v178_n2_p177_Andruskiewitsch_oai2024-08-16 Andruskiewitsch, N. Graña, M. 2003 A fundamental step in the classification of finite-dimensional complex pointed Hopf algebras is the determination of all finite-dimensional Nichols algebras of braided vector spaces arising from groups. The most important class of braided vector spaces arising from groups is the class of braided vector spaces (ℂX, cq), where X is a rack and q is a 2-cocycle on X with values in ℂx. Racks and cohomology of racks appeared also in the work of topologists. This leads us to the study of the structure of racks, their cohomology groups and the corresponding Nichols algebras. We will show advances in these three directions. We classify simple racks in group-theoretical terms; we describe projections of racks in terms of general cocycles; we introduce a general cohomology theory of racks containing properly the existing ones. We introduce a "Fourier transform" on racks of certain type; finally, we compute some new examples of finite-dimensional Nichols algebras. © 2003 Elsevier Inc. All rights reserved. Fil:Andruskiewitsch, N. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Graña, M. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. application/pdf http://hdl.handle.net/20.500.12110/paper_00018708_v178_n2_p177_Andruskiewitsch info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar Adv. Math. 2003;178(2):177-243 Pointed Hopf algebras Quandles Racks From racks to pointed Hopf algebras info:eu-repo/semantics/article info:ar-repo/semantics/artículo info:eu-repo/semantics/publishedVersion https://repositoriouba.sisbi.uba.ar/gsdl/cgi-bin/library.cgi?a=d&c=artiaex&d=paper_00018708_v178_n2_p177_Andruskiewitsch_oai
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-145
collection Repositorio Digital de la Universidad de Buenos Aires (UBA)
topic Pointed Hopf algebras
Quandles
Racks
spellingShingle Pointed Hopf algebras
Quandles
Racks
Andruskiewitsch, N.
Graña, M.
From racks to pointed Hopf algebras
topic_facet Pointed Hopf algebras
Quandles
Racks
description A fundamental step in the classification of finite-dimensional complex pointed Hopf algebras is the determination of all finite-dimensional Nichols algebras of braided vector spaces arising from groups. The most important class of braided vector spaces arising from groups is the class of braided vector spaces (ℂX, cq), where X is a rack and q is a 2-cocycle on X with values in ℂx. Racks and cohomology of racks appeared also in the work of topologists. This leads us to the study of the structure of racks, their cohomology groups and the corresponding Nichols algebras. We will show advances in these three directions. We classify simple racks in group-theoretical terms; we describe projections of racks in terms of general cocycles; we introduce a general cohomology theory of racks containing properly the existing ones. We introduce a "Fourier transform" on racks of certain type; finally, we compute some new examples of finite-dimensional Nichols algebras. © 2003 Elsevier Inc. All rights reserved.
format Artículo
Artículo
publishedVersion
author Andruskiewitsch, N.
Graña, M.
author_facet Andruskiewitsch, N.
Graña, M.
author_sort Andruskiewitsch, N.
title From racks to pointed Hopf algebras
title_short From racks to pointed Hopf algebras
title_full From racks to pointed Hopf algebras
title_fullStr From racks to pointed Hopf algebras
title_full_unstemmed From racks to pointed Hopf algebras
title_sort from racks to pointed hopf algebras
publishDate 2003
url http://hdl.handle.net/20.500.12110/paper_00018708_v178_n2_p177_Andruskiewitsch
https://repositoriouba.sisbi.uba.ar/gsdl/cgi-bin/library.cgi?a=d&c=artiaex&d=paper_00018708_v178_n2_p177_Andruskiewitsch_oai
work_keys_str_mv AT andruskiewitschn fromrackstopointedhopfalgebras
AT granam fromrackstopointedhopfalgebras
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