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 µ(na,c ) and for several pairs (a, c) we obtain µ(na,c ).