C#-IDEALS OF LIE ALGEBRAS

Abstract

Let $L$ be a finite dimensional Lie algebra. A subalgebra $H$ of $L$ is called a $c^{#}$-ideal of $L$, if there is an ideal $K$ of $L$ with $L=H+K$ and $Hcap K$ is a $CAP$-subalgebra of $L$. This is analogous to the concept of a $c^{#}$-normal subgroup of a finite group. Now, we consider the influence of this concept on the structure of finite dimentional Lie algebras.