Bounds for the dimension of the center factor in capable nilpotent Lie algebras of class two

Abstract

Let L be a finite-dimensional nilpotent Lie algebra of class two over a field of characteristic different from two. The aim of the present paper is to give an upper bound for the dimension of the center factor L/Z(L) of a capable Lie algebra L. As a result, we also find a lower bound for the dimension of the derived subalgebra L 2 for a capable Lie algebra L. Furthermore, we also give some criteria for determining the capability of L.