Proposed Method for Expressing Inner Derivations of Leibniz Algebras

This work is concerned with the computational perspective of a specific case of derivations, known as inner derivation mapping. In this regard, we propose an algebraic method to provide inner derivations for a finite-dimensional Leibniz algebra in matrix representation. The method is applied on four-dimensional complex Leibniz algebras obtained earlier to present comprehensive descriptions of their inner derivations. Additionally, we also exhibit the span basis of outer derivatives for these algebras.