Central derivation of some classes of Leibniz algebras

Abstract

In this study, we deal with central derivation of finite low dimensional Leibniz algebras. We provide some properties of the central derivation algebras. Description of the central derivation algebras, with their dimensions, for complex Leibniz algebras of dimensions two, three and four are given and summarized in tabular form. The result is then used to determine which centroid is decomposable or indecomposable.