ON A REFINEMENT OF ADOS THEOREM

In this paper we study the minimal dimension mu(g) of a faithful g-mod ule for n-dimensional Lie algebras g. This is an interesting invariant of g which is difficult to compute. It is desirable to obtain good bo unds for mu(g), especially for nilpotent Lie algebras We will determin e here mu(g) for certain Lie algebras and prove upper bounds in genera l. For nilpotent Lie algebras of dimension n, the bound n(n) + 1 is kn own. We now obtain mu(g) < alpha/root n2(n) with some constant alpha s imilar to 2.76287.