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

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On abelian subalgebras and ideals of maximal dimension in supersolvable Lie algebras. / Ceballos, Manuel; Towers, David.
In: Journal of Pure and Applied Algebra, Vol. 218, No. 3, 03.2014, p. 497-503.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Ceballos, M & Towers, D 2014, 'On abelian subalgebras and ideals of maximal dimension in supersolvable Lie algebras', Journal of Pure and Applied Algebra, vol. 218, no. 3, pp. 497-503. https://doi.org/10.1016/j.jpaa.2013.06.017

APA

Ceballos, M., & Towers, D. (2014). On abelian subalgebras and ideals of maximal dimension in supersolvable Lie algebras. Journal of Pure and Applied Algebra, 218(3), 497-503. https://doi.org/10.1016/j.jpaa.2013.06.017

Vancouver

Ceballos M, Towers D. On abelian subalgebras and ideals of maximal dimension in supersolvable Lie algebras. Journal of Pure and Applied Algebra. 2014 Mar;218(3):497-503. Epub 2013 Jul 27. doi: 10.1016/j.jpaa.2013.06.017

Author

Ceballos, Manuel ; Towers, David. / On abelian subalgebras and ideals of maximal dimension in supersolvable Lie algebras. In: Journal of Pure and Applied Algebra. 2014 ; Vol. 218, No. 3. pp. 497-503.

Bibtex

@article{b60918b9a3074fc091ed3b6e7ea980d9,
title = "On abelian subalgebras and ideals of maximal dimension in supersolvable Lie algebras",
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.",
keywords = "Lie algebras, abelian subalgebra, abelian ideal, solvable, supersolvable , nilpotent",
author = "Manuel Ceballos and David Towers",
note = "The final, definitive version of this article has been published in the Journal, Journal of Pure and Applied Algebra 218 (3), 2014, {\textcopyright} ELSEVIER.",
year = "2014",
month = mar,
doi = "10.1016/j.jpaa.2013.06.017",
language = "English",
volume = "218",
pages = "497--503",
journal = "Journal of Pure and Applied Algebra",
issn = "0022-4049",
publisher = "Elsevier",
number = "3",

}

RIS

TY - JOUR

T1 - On abelian subalgebras and ideals of maximal dimension in supersolvable Lie algebras

AU - Ceballos, Manuel

AU - Towers, David

N1 - The final, definitive version of this article has been published in the Journal, Journal of Pure and Applied Algebra 218 (3), 2014, © ELSEVIER.

PY - 2014/3

Y1 - 2014/3

N2 - 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.

AB - 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.

KW - Lie algebras

KW - abelian subalgebra

KW - abelian ideal

KW - solvable

KW - supersolvable

KW - nilpotent

U2 - 10.1016/j.jpaa.2013.06.017

DO - 10.1016/j.jpaa.2013.06.017

M3 - Journal article

VL - 218

SP - 497

EP - 503

JO - Journal of Pure and Applied Algebra

JF - Journal of Pure and Applied Algebra

SN - 0022-4049

IS - 3

ER -