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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Detalles Bibliográficos
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
Descripción
Sumario: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.