2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/73531The Z-grading determined by a long simple root of an affine or finite type Lie algebra arises from an adjoint or cominuscule representation of a lower rank semi-simple complex Lie algebra. Analysis of the relationship between the grading and the representation leads to an extension of Kac's construction of nontwisted affine Lie algebras.44 pages, 2 figuresRepresentation TheoryRings and Algebras17B10; 17B67; 17B70text