2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/126184We prove an explicit formula for the invariant $μ(\Lg)$ for finite-dimensional semisimple, and reductive Lie algebras $\Lg$ over $\C$. Here $μ(\Lg)$ is the minimal dimension of a faithful linear representation of $\Lg$. The result can be used to study Dynkin's classification of maximal reductive subalgebras of semisimple Lie algebras.Representation Theory17B20;17B10text