On n-maximal subalgebras of Lie algebras

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On n-maximal subalgebras of Lie algebras. / Towers, David.
In: Proceedings of the American Mathematical Society, Vol. 144, No. 4, 01.2016, p. 1457-1466.

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

Harvard

Towers, D 2016, 'On n-maximal subalgebras of Lie algebras', Proceedings of the American Mathematical Society, vol. 144, no. 4, pp. 1457-1466. https://doi.org/10.1090/proc/12821

APA

Towers, D. (2016). On n-maximal subalgebras of Lie algebras. Proceedings of the American Mathematical Society, 144(4), 1457-1466. https://doi.org/10.1090/proc/12821

Vancouver

Towers D. On n-maximal subalgebras of Lie algebras. Proceedings of the American Mathematical Society. 2016 Jan;144(4):1457-1466. Epub 2015 Aug 12. doi: 10.1090/proc/12821

Author

Towers, David. / On n-maximal subalgebras of Lie algebras. In: Proceedings of the American Mathematical Society. 2016 ; Vol. 144, No. 4. pp. 1457-1466.

Bibtex

@article{b4f1e4d445fa4d4eacb4b733f3e4d0bb,

title = "On n-maximal subalgebras of Lie algebras",

abstract = " A chain S_0 < S_1 < ... < S_n = L is a maximal chain if each S_i is a maximal subalgebra of S_{i+1}. The subalgebra S_0 in such a series is called an n-maximal subalgebra. There are many interesting results concerning the question of what certain intrinsic properties of the maximal subalgebras of a Lie algebra L imply about the structure of L itself. Here we consider whether similar results can be obtained by imposing conditions on the n-maximal subalgebras of L, where n>1.",

keywords = "Lie algebras, maximal subalgebra, $n$-maximal , Frattini ideal , solvable , supersolvable, nilpotent ",

author = "David Towers",

year = "2016",

month = jan,

doi = "10.1090/proc/12821",

language = "English",

volume = "144",

pages = "1457--1466",

journal = "Proceedings of the American Mathematical Society",

issn = "0002-9939",

publisher = "American Mathematical Society",

number = "4",

}

RIS

TY - JOUR

T1 - On n-maximal subalgebras of Lie algebras

AU - Towers, David

PY - 2016/1

Y1 - 2016/1

N2 - A chain S_0 < S_1 < ... < S_n = L is a maximal chain if each S_i is a maximal subalgebra of S_{i+1}. The subalgebra S_0 in such a series is called an n-maximal subalgebra. There are many interesting results concerning the question of what certain intrinsic properties of the maximal subalgebras of a Lie algebra L imply about the structure of L itself. Here we consider whether similar results can be obtained by imposing conditions on the n-maximal subalgebras of L, where n>1.

AB - A chain S_0 < S_1 < ... < S_n = L is a maximal chain if each S_i is a maximal subalgebra of S_{i+1}. The subalgebra S_0 in such a series is called an n-maximal subalgebra. There are many interesting results concerning the question of what certain intrinsic properties of the maximal subalgebras of a Lie algebra L imply about the structure of L itself. Here we consider whether similar results can be obtained by imposing conditions on the n-maximal subalgebras of L, where n>1.

KW - Lie algebras

KW - maximal subalgebra

KW - $n$-maximal

KW - Frattini ideal

KW - solvable

KW - supersolvable

KW - nilpotent

U2 - 10.1090/proc/12821

DO - 10.1090/proc/12821

M3 - Journal article

VL - 144

SP - 1457

EP - 1466

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 4

ER -

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