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

Ceballos, Manuel and Towers, David (2014) On abelian subalgebras and ideals of maximal dimension in supersolvable Lie algebras. Journal of Pure and Applied Algebra, 218 (3). pp. 497-503. ISSN 0022-4049

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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 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.

Item Type:
Journal Article
Journal or Publication Title:
Journal of Pure and Applied Algebra
Additional Information:
The final, definitive version of this article has been published in the Journal, Journal of Pure and Applied Algebra 218 (3), 2014, © ELSEVIER.
Uncontrolled Keywords:
/dk/atira/pure/subjectarea/asjc/2600/2602
Subjects:
ID Code:
67166
Deposited By:
Deposited On:
14 Oct 2013 07:56
Refereed?:
Yes
Published?:
Published
Last Modified:
28 Mar 2020 02:54