A characterization of 3-graded Lie algebras generated by a pair

We prove that any 3-graded Lie algebra generated by an element of degree −1 and another of degree 1 over a field K of characteristic zero is isomorphic to a 3-graded Lie subalgebra of endowed with its usual 3-gradation, for some p(t) K[t]. We also give a thorough description of the ideals in the free case.