Towers, David (2015) Subalgebras that cover or avoid chief factors of Lie algebras. Proceedings of the American Mathematical Society, 143 (8). pp. 3377-3385. ISSN 0002-9939
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Official URL: https://doi.org/10.1090/S0002-9939-2015-12533-6
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.
Item Type:
Journal Article
Journal or Publication Title:
Proceedings of the American Mathematical Society
Uncontrolled Keywords:
/dk/atira/pure/subjectarea/asjc/2600
Subjects:
Departments:
ID Code:
73332
Deposited By:
Deposited On:
09 Apr 2015 08:42
Refereed?:
Yes
Published?:
Published
Last Modified:
21 Sep 2023 01:40