On minimal faithful representations of a class of nilpotent lie algebras

Abstract

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