C#-IDEALS OF LIE ALGEBRAS

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 H ∩ 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.