2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/68482We define a special sort of weighted oriented graphs, signed quivers. Each of these yields a symmetric quiver, i.e., a quiver endowed with an involutive anti-automorphism and the inherited signs. We develop a representation theory of symmetric quivers, in particular we describe the indecomposable symmetric representations. Their dimensions constitute root systems corresponding to certain symmetrizable generalized Cartan matrices.20 pagesAlgebraic GeometryRepresentation Theory14L30; 16G20; 17B67; 20G20text