In the years 2010-2012 I developed, together with my collaborators and coauthors prof. A.Sorin and M. Trigiante a reseach project aimed at determining a general scheme for exact solutions of Black-Hole type to D=4 Supergravities with various degrees of supersymmetry and various matter-coupling set ups. The theory of Lie algebras was an essential ingredient in this research adventure that paralleled the previously developed one aimed at integrable cosmological models also framed within supergravity theory.