2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/203726It is shown that for inhomogeneous Lie algebras $\frak{g}=\frak{s}\overrightarrow{\oplus}_Λ(\dim Λ)L_{1}$ satisfying the condition $\mathcal{N}(\frak{g})=1$, the only Casimir operator can be explicitly constructed from the Maurer-Cartan equations by means of wedge products. It is shown that this constraint imposes sharp bounds for the dimension of the representation $R$. The procedure is generalized to compute also the rational invariant of some Lie algebras.High Energy Physics - Theorytext