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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Detalles Bibliográficos
Autores principales: Andruskiewitsch, Nicolás, Graña, Matías Alejo
Publicado: 2003
Materias:
Pointed Hopf algebras
Quandles
Racks
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00018708_v178_n2_p177_Andruskiewitsch
http://hdl.handle.net/20.500.12110/paper_00018708_v178_n2_p177_Andruskiewitsch
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_00018708_v178_n2_p177_Andruskiewitsch
record_format dspace
spelling paper:paper_00018708_v178_n2_p177_Andruskiewitsch2023-06-08T14:21:42Z From racks to pointed Hopf algebras Andruskiewitsch, Nicolás Graña, Matías Alejo Pointed Hopf algebras Quandles Racks 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. 2003 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00018708_v178_n2_p177_Andruskiewitsch http://hdl.handle.net/20.500.12110/paper_00018708_v178_n2_p177_Andruskiewitsch
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Pointed Hopf algebras
Quandles
Racks
spellingShingle Pointed Hopf algebras
Quandles
Racks
Andruskiewitsch, Nicolás
Graña, Matías Alejo
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.
author Andruskiewitsch, Nicolás
Graña, Matías Alejo
author_facet Andruskiewitsch, Nicolás
Graña, Matías Alejo
author_sort Andruskiewitsch, Nicolás
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 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00018708_v178_n2_p177_Andruskiewitsch
http://hdl.handle.net/20.500.12110/paper_00018708_v178_n2_p177_Andruskiewitsch
work_keys_str_mv AT andruskiewitschnicolas fromrackstopointedhopfalgebras
AT granamatiasalejo fromrackstopointedhopfalgebras
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