Minimal faithful representations of reductive Lie algebras
Abstract.We prove an explicit formula for the invariant 
$$\mu({\mathfrak{g}})$$
 for finite-dimensional semisimple, and reductive Lie algebras 
$${\mathfrak{g}}$$
 over 
$${\mathbb{C}}$$
 . Here 
$$\mu({\mathfrak{g}})$$
 is the minimal dimension of a faithful linear representation of 
$${\mathfrak{g}}$$
 . The result can be used to study Dynkin’s classification of maximal reductive subalgebras of semisimple Lie algebras.