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.

中文翻译：

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可解莱布尼茨代数的局部和 2-局部推导

我们证明了任何对可解莱布尼茨代数的局部推导，其互补空间的维数最大，模型或阿贝尔零基数都是一个推导。我们证明了具有 [公式：见文本] 维互补空间的可解莱布尼茨代数与阿贝尔 nilradicals，承认不是推导的局部推导。此外，研究了关于此类代数的[公式：见文本]-局部推导的类似问题，并给出了可解莱布尼茨代数的一个例子，使得任何[公式：见文本]-局部推导都是一个推导，但它承认局部不属于派生的派生。