2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/161129We give a uniform geometric realization for the cluster algebra of an arbitrary finite type with principal coefficients at an arbitrary acyclic seed. This algebra is realized as the coordinate ring of a certain reduced double Bruhat cell in the simply connected semisimple algebraic group of the same Cartan-Killing type. In this realization, the cluster variables appear as certain (generalized) principal minors.38 pages, 2 figures; v2: minor editorial changes, to appear in Transformation GroupsRings and AlgebrasRepresentation Theory16S99 (Primary); 17B20, 22E46 (Secondary)text