Finite-dimensional pointed Hopf algebras over finite simple groups of Lie type V : Mixed classes in Chevalley and Steinberg groups

We show that all classes that are neither semisimple nor unipotent in finite simple Chevalley or Steinberg groups different from PSLₙ(q) collapse (i.e. are never the support of a finite-dimensional Nichols algebra). As a consequence, we prove that the only finite-dimensional pointed Hopf algebra who...

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Autores: Andruskiewitsch, Nicolás, Carnovale, Giovanna, García, Gastón Andrés
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2021
País:Argentina
Institución:Universidad Nacional de La Plata
Repositorio:SEDICI (UNLP)
Idioma:inglés
OAI Identifier:oai:sedici.unlp.edu.ar:10915/132335
Acceso en línea:http://sedici.unlp.edu.ar/handle/10915/132335
Access Level:acceso abierto
Palabra clave:Matemática
Hopf algebras and their applications
Simple groups: alternating groups and groups of Lie type
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spelling Finite-dimensional pointed Hopf algebras over finite simple groups of Lie type V : Mixed classes in Chevalley and Steinberg groupsAndruskiewitsch, NicolásCarnovale, GiovannaGarcía, Gastón AndrésMatemáticaHopf algebras and their applicationsSimple groups: alternating groups and groups of Lie typeWe show that all classes that are neither semisimple nor unipotent in finite simple Chevalley or Steinberg groups different from PSLₙ(q) collapse (i.e. are never the support of a finite-dimensional Nichols algebra). As a consequence, we prove that the only finite-dimensional pointed Hopf algebra whose group of group-like elements is PSp₂ₙ(q), PΩ⁺₄ₙ, PΩ⁻₄ₙ, ³D₄(q), E₇(q), E₈(q), F₄(q), or G₂(q) with q even is the group algebra.Facultad de Ciencias Exactas2021-11info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionArticulohttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdf605-647http://sedici.unlp.edu.ar/handle/10915/132335enginfo:eu-repo/semantics/altIdentifier/issn/0025-2611info:eu-repo/semantics/altIdentifier/issn/1432-1785info:eu-repo/semantics/altIdentifier/doi/10.1007/s00229-020-01248-5info:eu-repo/semantics/reference/hdl/10915/102972info:eu-repo/semantics/reference/hdl/10915/129363info:eu-repo/semantics/reference/hdl/10915/132328info:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by/4.0/Creative Commons Attribution 4.0 International (CC BY 4.0)reponame:SEDICI (UNLP)instname:Universidad Nacional de La Platainstacron:UNLP2024-05-08T13:10:47Zoai:sedici.unlp.edu.ar:10915/132335Institucionalhttp://sedici.unlp.edu.ar/Universidad públicaNo correspondehttp://sedici.unlp.edu.ar/oai/snrdalira@sedici.unlp.edu.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:13292024-05-08 13:10:47.529SEDICI (UNLP) - Universidad Nacional de La Platafalse
dc.title.none.fl_str_mv Finite-dimensional pointed Hopf algebras over finite simple groups of Lie type V : Mixed classes in Chevalley and Steinberg groups
title Finite-dimensional pointed Hopf algebras over finite simple groups of Lie type V : Mixed classes in Chevalley and Steinberg groups
spellingShingle Finite-dimensional pointed Hopf algebras over finite simple groups of Lie type V : Mixed classes in Chevalley and Steinberg groups
Andruskiewitsch, Nicolás
Matemática
Hopf algebras and their applications
Simple groups: alternating groups and groups of Lie type
title_short Finite-dimensional pointed Hopf algebras over finite simple groups of Lie type V : Mixed classes in Chevalley and Steinberg groups
title_full Finite-dimensional pointed Hopf algebras over finite simple groups of Lie type V : Mixed classes in Chevalley and Steinberg groups
title_fullStr Finite-dimensional pointed Hopf algebras over finite simple groups of Lie type V : Mixed classes in Chevalley and Steinberg groups
title_full_unstemmed Finite-dimensional pointed Hopf algebras over finite simple groups of Lie type V : Mixed classes in Chevalley and Steinberg groups
title_sort Finite-dimensional pointed Hopf algebras over finite simple groups of Lie type V : Mixed classes in Chevalley and Steinberg groups
dc.creator.none.fl_str_mv Andruskiewitsch, Nicolás
Carnovale, Giovanna
García, Gastón Andrés
author Andruskiewitsch, Nicolás
author_facet Andruskiewitsch, Nicolás
Carnovale, Giovanna
García, Gastón Andrés
author_role author
author2 Carnovale, Giovanna
García, Gastón Andrés
author2_role author
author
dc.subject.none.fl_str_mv Matemática
Hopf algebras and their applications
Simple groups: alternating groups and groups of Lie type
topic Matemática
Hopf algebras and their applications
Simple groups: alternating groups and groups of Lie type
description We show that all classes that are neither semisimple nor unipotent in finite simple Chevalley or Steinberg groups different from PSLₙ(q) collapse (i.e. are never the support of a finite-dimensional Nichols algebra). As a consequence, we prove that the only finite-dimensional pointed Hopf algebra whose group of group-like elements is PSp₂ₙ(q), PΩ⁺₄ₙ, PΩ⁻₄ₙ, ³D₄(q), E₇(q), E₈(q), F₄(q), or G₂(q) with q even is the group algebra.
publishDate 2021
dc.date.none.fl_str_mv 2021-11
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
Articulo
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://sedici.unlp.edu.ar/handle/10915/132335
url http://sedici.unlp.edu.ar/handle/10915/132335
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/issn/0025-2611
info:eu-repo/semantics/altIdentifier/issn/1432-1785
info:eu-repo/semantics/altIdentifier/doi/10.1007/s00229-020-01248-5
info:eu-repo/semantics/reference/hdl/10915/102972
info:eu-repo/semantics/reference/hdl/10915/129363
info:eu-repo/semantics/reference/hdl/10915/132328
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
http://creativecommons.org/licenses/by/4.0/
Creative Commons Attribution 4.0 International (CC BY 4.0)
eu_rights_str_mv openAccess
rights_invalid_str_mv http://creativecommons.org/licenses/by/4.0/
Creative Commons Attribution 4.0 International (CC BY 4.0)
dc.format.none.fl_str_mv application/pdf
605-647
dc.source.none.fl_str_mv reponame:SEDICI (UNLP)
instname:Universidad Nacional de La Plata
instacron:UNLP
instname_str Universidad Nacional de La Plata
instacron_str UNLP
institution UNLP
reponame_str SEDICI (UNLP)
collection SEDICI (UNLP)
repository.name.fl_str_mv SEDICI (UNLP) - Universidad Nacional de La Plata
repository.mail.fl_str_mv alira@sedici.unlp.edu.ar
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