On Algorithms for Computing Derivations and Antiderivations of Leibniz Algebras

The concepts of antiderivation and biderivation were first introduced for right Leibniz algebras in 1993. In this paper, we extend these definitions to left Leibniz algebras and develop Maple software programs specifically for computing derivations and antiderivations of Leibniz algebras. As an application, we provide a complete classification of biderivations for non-Lie Leibniz algebras of dimensions up to three over the complex field.