Subalgebras that cover or avoid chief factors of Lie algebras

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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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:
ID Code:
73332
Deposited By:
Deposited On:
09 Apr 2015 08:42
Refereed?:
Yes
Published?:
Published
Last Modified:
24 Jun 2020 02:23