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 principales: Andruskiewitsch, Nicolás, Carnovale, Giovanna, García, Gastón Andrés
Formato: Articulo
Lenguaje:Inglés
Publicado: 2021
Materias:
Matemática
Hopf algebras and their applications
Simple groups: alternating groups and groups of Lie type
Acceso en línea:http://sedici.unlp.edu.ar/handle/10915/132335
Aporte de:
SEDICI (UNLP) de Universidad Nacional de La Plata
id I19-R120-10915-132335
record_format dspace
institution Universidad Nacional de La Plata
institution_str I-19
repository_str R-120
collection SEDICI (UNLP)
language Inglés
topic Matemática
Hopf algebras and their applications
Simple groups: alternating groups and groups of Lie type
spellingShingle Matemática
Hopf algebras and their applications
Simple groups: alternating groups and groups of Lie type
Andruskiewitsch, Nicolás
Carnovale, Giovanna
García, Gastón Andrés
Finite-dimensional pointed Hopf algebras over finite simple groups of Lie type V : Mixed classes in Chevalley and Steinberg groups
topic_facet 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.
format Articulo
Articulo
author Andruskiewitsch, Nicolás
Carnovale, Giovanna
García, Gastón Andrés
author_facet Andruskiewitsch, Nicolás
Carnovale, Giovanna
García, Gastón Andrés
author_sort Andruskiewitsch, Nicolás
title Finite-dimensional pointed Hopf algebras over finite simple groups of Lie type V : Mixed classes in Chevalley and Steinberg groups
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
publishDate 2021
url http://sedici.unlp.edu.ar/handle/10915/132335
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AT garciagastonandres finitedimensionalpointedhopfalgebrasoverfinitesimplegroupsoflietypevmixedclassesinchevalleyandsteinberggroups
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