On nichols algebras over PGL (2, q) and PSL (2, q)

We compute necessary conditions on YetterDrinfeld modules over the groups PGL(2, q) = PGL(2, q) and PSL(2, q) = PSL(2, q) to generate finite-dimensional Nichols algebras. This is a first step towards a classification of pointed Hopf algebras with group of group-likes isomorphic to one of these group...

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Detalles Bibliográficos
Autores principales: Graña, Matías Alejo, Vendramin, Leandro
Publicado: 2010
Materias:
Nichols algebra
Pointed Hopf algebra
Racks
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_02194988_v9_n2_p195_Freyre
http://hdl.handle.net/20.500.12110/paper_02194988_v9_n2_p195_Freyre
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_02194988_v9_n2_p195_Freyre
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spelling paper:paper_02194988_v9_n2_p195_Freyre2023-06-08T15:21:38Z On nichols algebras over PGL (2, q) and PSL (2, q) Graña, Matías Alejo Vendramin, Leandro Nichols algebra Pointed Hopf algebra Racks We compute necessary conditions on YetterDrinfeld modules over the groups PGL(2, q) = PGL(2, q) and PSL(2, q) = PSL(2, q) to generate finite-dimensional Nichols algebras. This is a first step towards a classification of pointed Hopf algebras with group of group-likes isomorphic to one of these groups. As a by-product of the techniques developed in this work, we prove that any finite-dimensional pointed Hopf algebra over the Mathieu groups M20 or M21 = PSL(3, 4) is the group algebra. © 2010 World Scientific Publishing Company. Fil:Graña, M. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Vendramin, L. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2010 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_02194988_v9_n2_p195_Freyre http://hdl.handle.net/20.500.12110/paper_02194988_v9_n2_p195_Freyre
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Nichols algebra
Pointed Hopf algebra
Racks
spellingShingle Nichols algebra
Pointed Hopf algebra
Racks
Graña, Matías Alejo
Vendramin, Leandro
On nichols algebras over PGL (2, q) and PSL (2, q)
topic_facet Nichols algebra
Pointed Hopf algebra
Racks
description We compute necessary conditions on YetterDrinfeld modules over the groups PGL(2, q) = PGL(2, q) and PSL(2, q) = PSL(2, q) to generate finite-dimensional Nichols algebras. This is a first step towards a classification of pointed Hopf algebras with group of group-likes isomorphic to one of these groups. As a by-product of the techniques developed in this work, we prove that any finite-dimensional pointed Hopf algebra over the Mathieu groups M20 or M21 = PSL(3, 4) is the group algebra. © 2010 World Scientific Publishing Company.
author Graña, Matías Alejo
Vendramin, Leandro
author_facet Graña, Matías Alejo
Vendramin, Leandro
author_sort Graña, Matías Alejo
title On nichols algebras over PGL (2, q) and PSL (2, q)
title_short On nichols algebras over PGL (2, q) and PSL (2, q)
title_full On nichols algebras over PGL (2, q) and PSL (2, q)
title_fullStr On nichols algebras over PGL (2, q) and PSL (2, q)
title_full_unstemmed On nichols algebras over PGL (2, q) and PSL (2, q)
title_sort on nichols algebras over pgl (2, q) and psl (2, q)
publishDate 2010
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_02194988_v9_n2_p195_Freyre
http://hdl.handle.net/20.500.12110/paper_02194988_v9_n2_p195_Freyre
work_keys_str_mv AT granamatiasalejo onnicholsalgebrasoverpgl2qandpsl2q
AT vendraminleandro onnicholsalgebrasoverpgl2qandpsl2q
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