2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/100810We study relations between finite-dimensional representations of color Lie algebras and their cocycle twists. Main tools are the universal enveloping algebras and their FCR-properties (finite-dimensional representations are completely reducible.) Cocycle twist preserves the FCR-property. As an application, we compute all finite dimensional representations (up to isomorphism) of the color Lie algebra $sl_2^c$.18 pages, with an concrete exampleRepresentation TheoryRings and Algebrastext