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.