2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/164701In this paper we study the minimal number of generators for simple Lie algebras in characteristic 0 or p > 3. We show that any such algebra can be generated by 2 elements. We also examine the 'one and a half generation' property, i.e. when every non-zero element can be completed to a generating pair. We show that classical simple algebras have this property, and that the only simple Cartan type algebras of type W which have this property are the Zassenhaus algebras.26 pages, final version, to appear in Math. Z. Main improvements and corrections in Section 4.3Representation TheoryAlgebraic GeometryRings and Algebras17B50; 17B45text