2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/61415The complete affine structures on abelian Lie algebras in small dimensions are well known. In this paper we are interested by the non complete case. In particular we classify all these structures in dimensions 2 and 3.14 pagesRings and AlgebrasDifferential Geometry17Bxx; 53Axxtext