2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/155936In this paper, we construct a faithful representation with the lowest dimension for every complex Lie algebra in dimension $\leq 4$. In particular, in our construction, in the case that the faithful representation has the same dimension of the Lie algebra, it can induce an étale affine representation with base zero which has a natural and simple form and gives a compatible left-symmetric algebra on the Lie algebra. Such affine representations do not contain any nontrivial one-parameter subgroups of translation.11 pages, 4 tables, appear in Communications in AlgebraQuantum AlgebraMathematical Physics17B, 53Ctext