Finite-dimensional pointed Hopf algebras over finite simple groups of Lie type V : Mixed classes in Chevalley and Steinberg groups
- Autores
- Andruskiewitsch, Nicolás; Carnovale, Giovanna; García, Gastón Andrés
- Año de publicación
- 2021
- Idioma
- inglés
- Tipo de recurso
- artículo
- Estado
- versión publicada
- Descripción
- 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.
Facultad de Ciencias Exactas - Materia
-
Matemática
Hopf algebras and their applications
Simple groups: alternating groups and groups of Lie type - Nivel de accesibilidad
- acceso abierto
- Condiciones de uso
- http://creativecommons.org/licenses/by/4.0/
- Repositorio
.jpg)
- Institución
- Universidad Nacional de La Plata
- OAI Identificador
- oai:sedici.unlp.edu.ar:10915/132335
Ver los metadatos del registro completo
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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:UNLP2025-10-22T17:13:20Zoai: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:13292025-10-22 17:13:21.17SEDICI (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 |
| dc.description.none.fl_txt_mv |
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. Facultad de Ciencias Exactas |
| 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 |
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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 |
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info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/4.0/ Creative Commons Attribution 4.0 International (CC BY 4.0) |
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openAccess |
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http://creativecommons.org/licenses/by/4.0/ Creative Commons Attribution 4.0 International (CC BY 4.0) |
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application/pdf 605-647 |
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