2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/183790The automorphisms of all 4-dimensional, real Lie Algebras are presented in a comprehensive way. Their action on the space of $4\times 4$, real, symmetric and positive definite, matrices, defines equivalence classes which are used for the invariant characterization of the 4-dimensional homogeneous spaces which possess an invariant basis.LaTeX2e, 23 pages, 2 Tables. To appear in Journal of Physics A: Mathematical & GeneralGeneral Relativity and Quantum CosmologyMathematical Physicstext