2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/168531Let g_A (respectively, g_A(μ)) be the graded multi-loop Lie algebra (respectively graded twisted multi-loop Lie algebra)" associated with the simple finite dimensional Lie algebra g over the complex field C. In this paper, we prove that irreducible integrable g_A(μ)-modules with finite dimensional weight spaces are either highest weight modules or their duals and classify the isomorphism classes of irreducible integrable g_A-modules and g_A(μ)-modules with finite dimensional weight spaces.Contents ChangedRepresentation TheoryRings and Algebrastext