From racks to pointed Hopf algebras

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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Detalhes bibliográficos
Autores: Andruskiewitsch, N., Graña, M.
Formato: artículo
Estado:Versión publicada
Fecha de publicación:2003
País:Argentina
Recursos:Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales
Repositorio:Biblioteca Digital (UBA-FCEN)
Idioma:inglés
OAI Identifier:paperaa:paper_00018708_v178_n2_p177_Andruskiewitsch
Acesso em linha:http://hdl.handle.net/20.500.12110/paper_00018708_v178_n2_p177_Andruskiewitsch
Access Level:acceso abierto
Palavra-chave:Pointed Hopf algebras
Quandles
Racks
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spelling From racks to pointed Hopf algebrasAndruskiewitsch, N.Graña, M.Pointed Hopf algebrasQuandlesRacksA 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.2003info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfhttp://hdl.handle.net/20.500.12110/paper_00018708_v178_n2_p177_AndruskiewitschAdv. Math. 2003;178(2):177-243reponame:Biblioteca Digital (UBA-FCEN)instname:Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturalesinstacron:UBA-FCENenginfo:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by/2.5/ar2024-05-10T10:42:41Zpaperaa:paper_00018708_v178_n2_p177_AndruskiewitschInstitucionalhttps://digital.bl.fcen.uba.ar/Universidad públicaNo correspondehttps://digital.bl.fcen.uba.ar/cgi-bin/oaiserver.cgiana@bl.fcen.uba.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:18962024-05-10 10:42:42.593Biblioteca Digital (UBA-FCEN) - Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturalesfalse
dc.title.none.fl_str_mv From racks to pointed Hopf algebras
title From racks to pointed Hopf algebras
spellingShingle From racks to pointed Hopf algebras
Andruskiewitsch, N.
Pointed Hopf algebras
Quandles
Racks
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
dc.creator.none.fl_str_mv Andruskiewitsch, N.
Graña, M.
author Andruskiewitsch, N.
author_facet Andruskiewitsch, N.
Graña, M.
author_role author
author2 Graña, M.
author2_role author
dc.subject.none.fl_str_mv Pointed Hopf algebras
Quandles
Racks
topic 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.
publishDate 2003
dc.date.none.fl_str_mv 2003
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/20.500.12110/paper_00018708_v178_n2_p177_Andruskiewitsch
url http://hdl.handle.net/20.500.12110/paper_00018708_v178_n2_p177_Andruskiewitsch
dc.language.none.fl_str_mv eng
language eng
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
http://creativecommons.org/licenses/by/2.5/ar
eu_rights_str_mv openAccess
rights_invalid_str_mv http://creativecommons.org/licenses/by/2.5/ar
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv Adv. Math. 2003;178(2):177-243
reponame:Biblioteca Digital (UBA-FCEN)
instname:Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales
instacron:UBA-FCEN
instname_str Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales
instacron_str UBA-FCEN
institution UBA-FCEN
reponame_str Biblioteca Digital (UBA-FCEN)
collection Biblioteca Digital (UBA-FCEN)
repository.name.fl_str_mv Biblioteca Digital (UBA-FCEN) - Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales
repository.mail.fl_str_mv ana@bl.fcen.uba.ar
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