2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/64170We prove that each real semisimple Lie algebra G has a Q-form, such that every real representation of G can be realized over the rational numbers Q. This was previously proved by M.S.Raghunathan (and rediscovered by P.Eberlein) in the special case where G is compact.21 pages, no figures, Latex2e file; added an alternate proof and strengthened the results in the final section, corrected minor errorsRepresentation Theory17B10; 22E47text