Investigation of ID-derivations of finite-dimensional nilpotent Lie algebras

Abstract

Let [Formula: see text] be a Lie algebra and let [Formula: see text] be the set of all derivations of [Formula: see text]. Then the derivation [Formula: see text] of [Formula: see text] is called an ID-derivation if [Formula: see text] for all [Formula: see text]. The set of all ID-derivations is denoted by [Formula: see text]. Let [Formula: see text] be the set of all central derivations and let [Formula: see text] and [Formula: see text] be, respectively, the set of all center derivations and ID-derivations that map [Formula: see text] to zero. In this paper, we verify relations between [Formula: see text] and [Formula: see text] with [Formula: see text] and [Formula: see text]. Also, we prove that if [Formula: see text] is a nilpotent Lie algebra of class [Formula: see text], then [Formula: see text] is a nilpotent Lie algebra of class [Formula: see text].