Local and 2-local derivations of solvable Leibniz algebras

Abstract

We show that any local derivation on the solvable Leibniz algebras with model or abelian nilradicals, whose dimension of complementary space is maximal is a derivation. We show that solvable Leibniz algebras with abelian nilradicals, which have [Formula: see text] dimension complementary space, admit local derivations which are not derivations. Moreover, similar problem concerning [Formula: see text]-local derivations of such algebras is investigated and an example of solvable Leibniz algebra is given such that any [Formula: see text]-local derivation on it is a derivation, but which admits local derivations which are not derivations.