Casimir operators induced by Maurer-Cartan equations
  It is shown that for inhomogeneous Lie algebras $\frak{g}=\frak{s}\overrightarrow{\oplus}_{\Lambda}(\dim \Lambda)L_{1}$ 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. 
R. Campoamor-Stursberg