Geodesic
On Equality of Certain Derivations of Lie Algebras
Discussiones Mathematicae. General Algebra and Applications, Tome 39 (2019) no. 2, pp. 153-164

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Let L be a Lie algebra. A derivation α of L is a commuting derivation (central derivation), if α (x) ∈ CL (x) (α (x) ∈ Z (L)) for each x ∈ L. We denote the set of all commuting derivations (central derivations) by (L) (Derz (L)). In this paper, first we show (L) is subalgebra from derivation algebra L, also we investigate the conditions on the Lie algebra L where commuting derivation is trivial and finally we introduce the family of nilpotent Lie algebras in which Derz (L) = (L).
Keywords: derivation, central derivation, centralizer, commuting derivation 
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Amiri, Azita; Saeedi, Farshid; Alemi, Mohammad Reza. On Equality of Certain Derivations of Lie Algebras. Discussiones Mathematicae. General Algebra and Applications, Tome 39 (2019) no. 2, pp. 153-164. http://geodesic.mathdoc.fr/item/DMGAA_2019_39_2_a0/