2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/223746In this paper we initiate a general classification for Lie algebras of order 3 and we give all Lie algebras of order 3 based on $\mathfrak{sl}(2,\mathbb C)$ and $\mathfrak{iso}(1,3)$ the Poincaré algebra in four-dimensions. We then set the basis of the theory of the deformations (in the Gerstenhaber sense) and contractions for Lie algebras of order 3.Title and presentation changedMathematical PhysicsHigh Energy Physics - Theory17A40; 17A42; 17A70; 17B81text