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    Rights statement: The final, definitive version of this article has been published in the Journal, Communications in Algebra, 41 (10), 2013, © Informa Plc

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Supplements to maximal subalgebras of Lie algebras

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Supplements to maximal subalgebras of Lie algebras. / Towers, David A.
In: Communications in Algebra, Vol. 41, No. 10, 10.2013, p. 3848-3857.

Research output: Contribution to Journal/Magazine › Journal article

Harvard

Towers, DA 2013, 'Supplements to maximal subalgebras of Lie algebras', Communications in Algebra, vol. 41, no. 10, pp. 3848-3857. https://doi.org/10.1080/00927872.2012.680206

APA

Towers, D. A. (2013). Supplements to maximal subalgebras of Lie algebras. Communications in Algebra, 41(10), 3848-3857. https://doi.org/10.1080/00927872.2012.680206

Vancouver

Towers DA. Supplements to maximal subalgebras of Lie algebras. Communications in Algebra. 2013 Oct;41(10):3848-3857. Epub 2013 Jul 26. doi: 10.1080/00927872.2012.680206

Author

Towers, David A. / Supplements to maximal subalgebras of Lie algebras. In: Communications in Algebra. 2013 ; Vol. 41, No. 10. pp. 3848-3857.

Bibtex

@article{ac8fa85278524a76b4cc5c6511c3d1ee,
title = "Supplements to maximal subalgebras of Lie algebras",
abstract = "For a Lie algebra L and a subalgebra M of L we say that a subalgebra U of L is a supplement to M in L if L = M +U. We investigate those Lie algebras all of whose maximal subalgebras have abelian supplements, those that have nilpotent supplements, those that have nil supplements, and those that have supplements with the property that their derived algebra is inside the maximal subalgebra being supplemented. For the algebras over an algebraically closed field of characteristic zero in the last three of these classes we find complete descriptions; for those in the first class partial results are obtained.",
keywords = "Lie algebras, maximal subalgebra, supplement, solvable, supersolvable, Frattini ideal.",
author = "Towers, {David A.}",
note = "The final, definitive version of this article has been published in the Journal, Communications in Algebra, 41 (10), 2013, {\textcopyright} Informa Plc",
year = "2013",
month = oct,
doi = "10.1080/00927872.2012.680206",
language = "English",
volume = "41",
pages = "3848--3857",
journal = "Communications in Algebra",
issn = "0092-7872",
publisher = "Taylor and Francis Ltd.",
number = "10",

}

RIS

TY - JOUR

T1 - Supplements to maximal subalgebras of Lie algebras

AU - Towers, David A.

N1 - The final, definitive version of this article has been published in the Journal, Communications in Algebra, 41 (10), 2013, © Informa Plc

PY - 2013/10

Y1 - 2013/10

N2 - For a Lie algebra L and a subalgebra M of L we say that a subalgebra U of L is a supplement to M in L if L = M +U. We investigate those Lie algebras all of whose maximal subalgebras have abelian supplements, those that have nilpotent supplements, those that have nil supplements, and those that have supplements with the property that their derived algebra is inside the maximal subalgebra being supplemented. For the algebras over an algebraically closed field of characteristic zero in the last three of these classes we find complete descriptions; for those in the first class partial results are obtained.

AB - For a Lie algebra L and a subalgebra M of L we say that a subalgebra U of L is a supplement to M in L if L = M +U. We investigate those Lie algebras all of whose maximal subalgebras have abelian supplements, those that have nilpotent supplements, those that have nil supplements, and those that have supplements with the property that their derived algebra is inside the maximal subalgebra being supplemented. For the algebras over an algebraically closed field of characteristic zero in the last three of these classes we find complete descriptions; for those in the first class partial results are obtained.

KW - Lie algebras

KW - maximal subalgebra

KW - supplement

KW - solvable

KW - supersolvable

KW - Frattini ideal.

U2 - 10.1080/00927872.2012.680206

DO - 10.1080/00927872.2012.680206

M3 - Journal article

VL - 41

SP - 3848

EP - 3857

JO - Communications in Algebra

JF - Communications in Algebra

SN - 0092-7872

IS - 10

ER -