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.

References in corpus (1)

• Generators of simple Lie algebras in arbitrary characteristics

Cited by in corpus (1)

• C-sections of Lie algebras