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    Rights statement: This is an Accepted Manuscript of an article published by Taylor & Francis in Linear and Multilinear Algebra on 20/08/2020, available online: https://www.tandfonline.com/doi/abs/10.1080/03081087.2020.1805399

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Abelian subalgebras and ideals of maximal dimension in supersolvable and nilpotent Lie algebras

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

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Abelian subalgebras and ideals of maximal dimension in supersolvable and nilpotent Lie algebras. / Towers, David.
In: Linear and Multilinear Algebra, Vol. 70, No. 13, 30.09.2022, p. 2551-2568.

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

Harvard

Towers, D 2022, 'Abelian subalgebras and ideals of maximal dimension in supersolvable and nilpotent Lie algebras', Linear and Multilinear Algebra, vol. 70, no. 13, pp. 2551-2568. https://doi.org/10.1080/03081087.2020.1805399

APA

Towers, D. (2022). Abelian subalgebras and ideals of maximal dimension in supersolvable and nilpotent Lie algebras. Linear and Multilinear Algebra, 70(13), 2551-2568. https://doi.org/10.1080/03081087.2020.1805399

Vancouver

Towers D. Abelian subalgebras and ideals of maximal dimension in supersolvable and nilpotent Lie algebras. Linear and Multilinear Algebra. 2022 Sept 30;70(13):2551-2568. Epub 2020 Aug 20. doi: 10.1080/03081087.2020.1805399

Author

Towers, David. / Abelian subalgebras and ideals of maximal dimension in supersolvable and nilpotent Lie algebras. In: Linear and Multilinear Algebra. 2022 ; Vol. 70, No. 13. pp. 2551-2568.

Bibtex

@article{6453f5473bed4db8b26f15bb05c9c152,
title = "Abelian subalgebras and ideals of maximal dimension in supersolvable and nilpotent Lie algebras",
abstract = "In this paper, we continue the study of abelian subalgebras andideals of maximal dimension for finite-dimensional supersolvable andnilpotent Lie algebras. We show that supersolvable Lie algebras withan abelian subalgebra of codimension 3 contain an abelian ideal withthe same dimension, provided that the characteristic of the underlyingfield is not two, and that the same is true for nilpotent Lie algebraswith an abelian subalgebra of codimension 4, provided that the char-acteristic of the field is greater than five.",
keywords = "Lie algebras, Abelian subalgebra, Abelian ideal, Solvable, Supersolvable, Nilpotent",
author = "David Towers",
note = "This is an Accepted Manuscript of an article published by Taylor & Francis in Linear and Multilinear Algebra on 20/08/2020, available online: https://www.tandfonline.com/doi/abs/10.1080/03081087.2020.1805399",
year = "2022",
month = sep,
day = "30",
doi = "10.1080/03081087.2020.1805399",
language = "English",
volume = "70",
pages = "2551--2568",
journal = "Linear and Multilinear Algebra",
issn = "0308-1087",
publisher = "Taylor and Francis Ltd.",
number = "13",

}

RIS

TY - JOUR

T1 - Abelian subalgebras and ideals of maximal dimension in supersolvable and nilpotent Lie algebras

AU - Towers, David

N1 - This is an Accepted Manuscript of an article published by Taylor & Francis in Linear and Multilinear Algebra on 20/08/2020, available online: https://www.tandfonline.com/doi/abs/10.1080/03081087.2020.1805399

PY - 2022/9/30

Y1 - 2022/9/30

N2 - In this paper, we continue the study of abelian subalgebras andideals of maximal dimension for finite-dimensional supersolvable andnilpotent Lie algebras. We show that supersolvable Lie algebras withan abelian subalgebra of codimension 3 contain an abelian ideal withthe same dimension, provided that the characteristic of the underlyingfield is not two, and that the same is true for nilpotent Lie algebraswith an abelian subalgebra of codimension 4, provided that the char-acteristic of the field is greater than five.

AB - In this paper, we continue the study of abelian subalgebras andideals of maximal dimension for finite-dimensional supersolvable andnilpotent Lie algebras. We show that supersolvable Lie algebras withan abelian subalgebra of codimension 3 contain an abelian ideal withthe same dimension, provided that the characteristic of the underlyingfield is not two, and that the same is true for nilpotent Lie algebraswith an abelian subalgebra of codimension 4, provided that the char-acteristic of the field is greater than five.

KW - Lie algebras

KW - Abelian subalgebra

KW - Abelian ideal

KW - Solvable

KW - Supersolvable

KW - Nilpotent

U2 - 10.1080/03081087.2020.1805399

DO - 10.1080/03081087.2020.1805399

M3 - Journal article

VL - 70

SP - 2551

EP - 2568

JO - Linear and Multilinear Algebra

JF - Linear and Multilinear Algebra

SN - 0308-1087

IS - 13

ER -