2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/68830The main goal is to classify 4-dimensional real Lie algebras $\g$ which admit a para-hypercomplex structure. This is a step toward the classification of Lie groups admitting the corresponding left-invariant structure and therefore possessing a neutral, left-invariant, anti-self-dual metric. Our study is related to the work of Barberis who classified real, 4-dimensional simply-connected Lie groups which admit an invariant hypercomplex structure.15 pagesDifferential Geometry53C50, 53C56, 32M10, 53C26, 53C55text