On abelian subalgebras and ideals of maximal dimension in supersolvable Lie algebras

In this paper, the main objective is to compare the abelian subalgebras and ideals of maximal dimension for finite-dimensional supersolvable Lie algebras. We characterise the maximal abelian subalgebras of solvable Lie algebras and study solvable Lie algebras containing an abelian subalgebra of codi...

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Detalhes bibliográficos
Autores: Ceballos González, Manuel, Towers, David A.
Formato: artículo
Estado:Versión enviada para evaluación y publicación
Fecha de publicación:2014
País:España
Recursos:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/42618
Acesso em linha:http://hdl.handle.net/11441/42618
https://doi.org/10.1016/j.jpaa.2013.06.017
Access Level:acceso abierto
Palavra-chave:Lie algebras
abelian subalgebra
abelian ideal
solvable
supersolvable
nilpotent
Descrição
Resumo:In this paper, the main objective is to compare the abelian subalgebras and ideals of maximal dimension for finite-dimensional supersolvable Lie algebras. We characterise the maximal abelian subalgebras of solvable Lie algebras and study solvable Lie algebras containing an abelian subalgebra of codimension 2. Finally, we prove that nilpotent Lie algebras with an abelian subalgebra of codimension 3 contain an abelian ideal with the same dimension, provided that the characteristic of the underlying field is not two. Throughout the paper, we also give several examples to clarify some results.