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

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.