2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/69018A study is made of real Lie algebras admitting a hypersymplectic structure, and we provide a method to construct such hypersymplectic Lie algebras. We use this method in order to obtain the classification of all hypersymplectic structures on four-dimensional Lie algebras, and we describe the associated metrics on the corresponding Lie groups.Differential Geometry17B60, 53C15, 53C30, 53C50text