A classification of Nichols algebras of semisimple Yetter-Drinfeld modules over non-abelian groups

Over fields of arbitrary characteristic we classify all braid-indecomposable tuples of at least two absolutely simple Yetter-Drinfeld modules over non-abelian groups such that the group is generated by the support of the tuple and the Nichols algebra of the tuple is finite-dimensional. Such tuples a...

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Autores principales: Heckenberger, I., Vendramin, L.
Formato: JOUR
Materias:
Hopf algebra
Nichols algebra
Weyl groupoid
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_14359855_v19_n2_p299_Heckenberger
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
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spelling todo:paper_14359855_v19_n2_p299_Heckenberger2023-10-03T16:15:54Z A classification of Nichols algebras of semisimple Yetter-Drinfeld modules over non-abelian groups Heckenberger, I. Vendramin, L. Hopf algebra Nichols algebra Weyl groupoid Over fields of arbitrary characteristic we classify all braid-indecomposable tuples of at least two absolutely simple Yetter-Drinfeld modules over non-abelian groups such that the group is generated by the support of the tuple and the Nichols algebra of the tuple is finite-dimensional. Such tuples are classified in terms of analogs of Dynkin diagrams which encode much information about the Yetter-Drinfeld modules. We also compute the dimensions of these finite-dimensional Nichols algebras. Our proof uses essentially theWeyl groupoid of a tuple of simple Yetter-Drinfeld modules and our previous result on pairs. © European Mathematical Society 2017. Fil:Vendramin, L. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_14359855_v19_n2_p299_Heckenberger
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Hopf algebra
Nichols algebra
Weyl groupoid
spellingShingle Hopf algebra
Nichols algebra
Weyl groupoid
Heckenberger, I.
Vendramin, L.
A classification of Nichols algebras of semisimple Yetter-Drinfeld modules over non-abelian groups
topic_facet Hopf algebra
Nichols algebra
Weyl groupoid
description Over fields of arbitrary characteristic we classify all braid-indecomposable tuples of at least two absolutely simple Yetter-Drinfeld modules over non-abelian groups such that the group is generated by the support of the tuple and the Nichols algebra of the tuple is finite-dimensional. Such tuples are classified in terms of analogs of Dynkin diagrams which encode much information about the Yetter-Drinfeld modules. We also compute the dimensions of these finite-dimensional Nichols algebras. Our proof uses essentially theWeyl groupoid of a tuple of simple Yetter-Drinfeld modules and our previous result on pairs. © European Mathematical Society 2017.
format JOUR
author Heckenberger, I.
Vendramin, L.
author_facet Heckenberger, I.
Vendramin, L.
author_sort Heckenberger, I.
title A classification of Nichols algebras of semisimple Yetter-Drinfeld modules over non-abelian groups
title_short A classification of Nichols algebras of semisimple Yetter-Drinfeld modules over non-abelian groups
title_full A classification of Nichols algebras of semisimple Yetter-Drinfeld modules over non-abelian groups
title_fullStr A classification of Nichols algebras of semisimple Yetter-Drinfeld modules over non-abelian groups
title_full_unstemmed A classification of Nichols algebras of semisimple Yetter-Drinfeld modules over non-abelian groups
title_sort classification of nichols algebras of semisimple yetter-drinfeld modules over non-abelian groups
url http://hdl.handle.net/20.500.12110/paper_14359855_v19_n2_p299_Heckenberger
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