2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/126570Given an orientable weakly self-dual manifold X of rank two, we build a geometric realization of the Lie algebra sl(6,C) as a naturally defined algebra L of endomorphisms of the space of differential forms of X. We provide an explicit description of Serre generators in terms of natural generators of L. This construction gives a bundle on X which is related to the search for a natural Gauge theory on X. We consider this paper as a first step in the study of a rich and interesting algebraic structure.16 pages, no figuresDifferential GeometryRepresentation Theory53A45; 15A66; 20C15text