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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| Formato: | Artículo publishedVersion |
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2003
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| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_00018708_v178_n2_p177_Andruskiewitsch |
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paperaa:paper_00018708_v178_n2_p177_Andruskiewitsch2023-06-12T16:39:26Z From racks to pointed Hopf algebras Adv. Math. 2003;178(2):177-243 Andruskiewitsch, N. Graña, M. 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 info:eu-repo/semantics/article info:ar-repo/semantics/artículo info:eu-repo/semantics/publishedVersion application/pdf eng info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar 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) |
| language |
Inglés |
| orig_language_str_mv |
eng |
| 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 |
| work_keys_str_mv |
AT andruskiewitschn fromrackstopointedhopfalgebras AT granam fromrackstopointedhopfalgebras |
| _version_ |
1769810200431165440 |