  We study the problem of extending a complex structure to a given Lie algebra
g, which is firstly defined on an ideal h of g. We consider the next
situations: h is either complex or it is totally real. The next question is to
equip g with an additional structure, such as a (non)-definite metric or a
symplectic structure and to ask either h is non-degenerate, isotropic, etc.
with respect to this structure, by imposing a compatibility assumption. We show
that this implies certain constraints on the algebraic structure of g.
Constructive examples illustrating this situation are shown, in particular
computations in dimension six are given.
