Lie algebras with a set grading

Consider gg a Lie algebra graded by an arbitrary set I   (set grading). We show that gg decomposes as the sum of well-described graded ideals plus (maybe) a certain linear subspace. Under mild conditions, the simplicity of gg is characterized and it is shown that the above decomposition is actually the direct sum of the family of its minimal graded ideals (each one being a simple set-graded Lie algebra).