Subalgebras that cover or avoid chief factors of Lie algebras

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Subalgebras that cover or avoid chief factors of Lie algebras. / Towers, David.
In: Proceedings of the American Mathematical Society, Vol. 143, No. 8, 2015, p. 3377-3385.

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

Harvard

Towers, D 2015, 'Subalgebras that cover or avoid chief factors of Lie algebras', Proceedings of the American Mathematical Society, vol. 143, no. 8, pp. 3377-3385. https://doi.org/10.1090/S0002-9939-2015-12533-6

APA

Towers, D. (2015). Subalgebras that cover or avoid chief factors of Lie algebras. Proceedings of the American Mathematical Society, 143(8), 3377-3385. https://doi.org/10.1090/S0002-9939-2015-12533-6

Vancouver

Towers D. Subalgebras that cover or avoid chief factors of Lie algebras. Proceedings of the American Mathematical Society. 2015;143(8):3377-3385. Epub 2015 Mar 18. doi: 10.1090/S0002-9939-2015-12533-6

Author

Towers, David. / Subalgebras that cover or avoid chief factors of Lie algebras. In: Proceedings of the American Mathematical Society. 2015 ; Vol. 143, No. 8. pp. 3377-3385.

Bibtex

@article{980eb124d7254e7da397e3374447791a,

title = "Subalgebras that cover or avoid chief factors of Lie algebras",

abstract = "We call a subalgebra $U$ of a Lie algebra $L$ a $CAP$-subalgebra of $L$ if for any chief factor $H/K$ of $L$, we have $H \cap U = K \cap U$ or $H+U = K+U$. In this paper we investigate some properties of such subalgebras and obtain some characterizations for a finite-dimensional Lie algebra $L$ to be solvable under the assumption that some of its maximal subalgebras or $2$-maximal subalgebras be $CAP$-subalgebras.",

keywords = " Lie algebras, solvable, chief factor, cover, avoid",

author = "David Towers",

year = "2015",

doi = "10.1090/S0002-9939-2015-12533-6",

language = "English",

volume = "143",

pages = "3377--3385",

journal = "Proceedings of the American Mathematical Society",

issn = "0002-9939",

publisher = "American Mathematical Society",

number = "8",

}

RIS

TY - JOUR

T1 - Subalgebras that cover or avoid chief factors of Lie algebras

AU - Towers, David

PY - 2015

Y1 - 2015

N2 - We call a subalgebra $U$ of a Lie algebra $L$ a $CAP$-subalgebra of $L$ if for any chief factor $H/K$ of $L$, we have $H \cap U = K \cap U$ or $H+U = K+U$. In this paper we investigate some properties of such subalgebras and obtain some characterizations for a finite-dimensional Lie algebra $L$ to be solvable under the assumption that some of its maximal subalgebras or $2$-maximal subalgebras be $CAP$-subalgebras.

AB - We call a subalgebra $U$ of a Lie algebra $L$ a $CAP$-subalgebra of $L$ if for any chief factor $H/K$ of $L$, we have $H \cap U = K \cap U$ or $H+U = K+U$. In this paper we investigate some properties of such subalgebras and obtain some characterizations for a finite-dimensional Lie algebra $L$ to be solvable under the assumption that some of its maximal subalgebras or $2$-maximal subalgebras be $CAP$-subalgebras.

KW - Lie algebras

KW - solvable

KW - chief factor

KW - cover

KW - avoid

U2 - 10.1090/S0002-9939-2015-12533-6

DO - 10.1090/S0002-9939-2015-12533-6

M3 - Journal article

VL - 143

SP - 3377

EP - 3385

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 8

ER -

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