Article
On abelian subalgebras and ideals of maximal dimension in supersolvable Lie algebras
Author/s | Ceballos González, Manuel
Towers, David A. |
Department | Universidad de Sevilla. Departamento de Geometría y Topología |
Date | 2014-02 |
Published in |
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Abstract | 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 ... 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. |
Funding agencies | Ministerio de Ciencia e Innovación (MICIN). España European Commission (EC). Fondo Europeo de Desarrollo Regional (FEDER) |
Project ID. | MTM2010-19336
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Citation | Ceballos González, M. y Towers, D.A. (2014). On abelian subalgebras and ideals of maximal dimension in supersolvable Lie algebras. Journal of Pure and Applied Algebra, 218 (3), 497-503. |
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