On Minimal Faithful Representations of a Class of Nilpotent Lie Algebras

In this work we consider 2-step nilradicals of parabolic subalgebras of the simple Lie algebra A(n) and describe a new family of faithful nil-representations of the nilradicals n(a,c), a, c is an element of N. We obtain a sharp upper bound for the minimal dimension mu(n(a,c)) and for several pairs (a, c) we obtain mu(n(a,c)).