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Maximal subalgebras and chief factors of Lie algebras

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Maximal subalgebras and chief factors of Lie algebras. / Towers, David.
In: Journal of Pure and Applied Algebra, Vol. 220, No. 1, 01.2016, p. 482-493.

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

Harvard

Towers, D 2016, 'Maximal subalgebras and chief factors of Lie algebras', Journal of Pure and Applied Algebra, vol. 220, no. 1, pp. 482-493. https://doi.org/10.1016/j.jpaa.2015.07.005

APA

Towers, D. (2016). Maximal subalgebras and chief factors of Lie algebras. Journal of Pure and Applied Algebra, 220(1), 482-493. https://doi.org/10.1016/j.jpaa.2015.07.005

Vancouver

Towers D. Maximal subalgebras and chief factors of Lie algebras. Journal of Pure and Applied Algebra. 2016 Jan;220(1):482-493. Epub 2015 Jul 29. doi: 10.1016/j.jpaa.2015.07.005

Author

Towers, David. / Maximal subalgebras and chief factors of Lie algebras. In: Journal of Pure and Applied Algebra. 2016 ; Vol. 220, No. 1. pp. 482-493.

Bibtex

@article{6b370c0b00804738b7888ed485820459,
title = "Maximal subalgebras and chief factors of Lie algebras",
abstract = "This paper is a continued investigation of the structure of Lie algebras in relation to their chief factors, using concepts that are analogous to corresponding ones in group theory. The first section investigates the structure of Lie algebras with a core-free maximal subalgebra. The results obtained are then used in section two to consider the relationship of two chief factors of L being L-connected, a weaker equivalence relation on the set of chief factors than that of being isomorphic as L-modules. A strengthened form of the Jordan-Holder Theorem in which Frattini chief factors correspond is also established for every Lie algebra. The final section introduces the concept of a crown, a notionintroduced in group theory by Gaschutz, and shows that it gives much information about the chief factors",
keywords = "Lie algebras, maximal subalgebra, core-free, chief factor, crown, prefrattini subalgebras",
author = "David Towers",
year = "2016",
month = jan,
doi = "10.1016/j.jpaa.2015.07.005",
language = "English",
volume = "220",
pages = "482--493",
journal = "Journal of Pure and Applied Algebra",
issn = "0022-4049",
publisher = "Elsevier",
number = "1",

}

RIS

TY - JOUR

T1 - Maximal subalgebras and chief factors of Lie algebras

AU - Towers, David

PY - 2016/1

Y1 - 2016/1

N2 - This paper is a continued investigation of the structure of Lie algebras in relation to their chief factors, using concepts that are analogous to corresponding ones in group theory. The first section investigates the structure of Lie algebras with a core-free maximal subalgebra. The results obtained are then used in section two to consider the relationship of two chief factors of L being L-connected, a weaker equivalence relation on the set of chief factors than that of being isomorphic as L-modules. A strengthened form of the Jordan-Holder Theorem in which Frattini chief factors correspond is also established for every Lie algebra. The final section introduces the concept of a crown, a notionintroduced in group theory by Gaschutz, and shows that it gives much information about the chief factors

AB - This paper is a continued investigation of the structure of Lie algebras in relation to their chief factors, using concepts that are analogous to corresponding ones in group theory. The first section investigates the structure of Lie algebras with a core-free maximal subalgebra. The results obtained are then used in section two to consider the relationship of two chief factors of L being L-connected, a weaker equivalence relation on the set of chief factors than that of being isomorphic as L-modules. A strengthened form of the Jordan-Holder Theorem in which Frattini chief factors correspond is also established for every Lie algebra. The final section introduces the concept of a crown, a notionintroduced in group theory by Gaschutz, and shows that it gives much information about the chief factors

KW - Lie algebras

KW - maximal subalgebra

KW - core-free

KW - chief factor

KW - crown

KW - prefrattini subalgebras

U2 - 10.1016/j.jpaa.2015.07.005

DO - 10.1016/j.jpaa.2015.07.005

M3 - Journal article

VL - 220

SP - 482

EP - 493

JO - Journal of Pure and Applied Algebra

JF - Journal of Pure and Applied Algebra

SN - 0022-4049

IS - 1

ER -