Some Properties of ID- L i e -derivations of Leibniz algebras

The concepts of Lie-derivations and Lie-central derivations have been recently presented in [G. R. Biyogmam and J. M. Casas, Lie-central derivations, Lie-centroids and Lie-stem Leibniz algebras, Publ. Math. Debrecen 97(1-2) (2020) 217-239]. This paper studies the notions of n-Lie-derivation and n-Lie-central derivation on Leibniz algebras as generalizations of these concepts. It is shown that under some conditions, n-Lie-central derivations of a non-Lie-Leibniz algebra coincide with ID-n-Lie-derivations, that is, n-Lie-derivations in which the image is contained in the (n + 1)th term of the lower Lie-central series of , and vanishes on the upper Lie-central series of . We prove some properties of these ID-n-Lie-derivations. In particular, it is shown that the Lie algebra structure of the set of ID-n-Lie-derivations is preserved under n-Lie-isoclinism.