On Algorithms for Computing Derivations and Antiderivations of Leibniz Algebras

Pawaran Hongsopa; Pattrawadee Janplee; Chanisata Kimsang; Suchada Pongprasert; Nissara Sirasuntorn

Authors

Pawaran Hongsopa Department of Mathematics, Faculty of Science, Srinakharinwirot University, Bangkok 10110, Thailand
Pattrawadee Janplee Department of Mathematics, Faculty of Science, Srinakharinwirot University, Bangkok 10110, Thailand
Chanisata Kimsang Department of Mathematics, Faculty of Science, Srinakharinwirot University, Bangkok 10110, Thailand
Suchada Pongprasert Department of Mathematics, Faculty of Science, Srinakharinwirot University, Bangkok 10110, Thailand
Nissara Sirasuntorn Department of Mathematics, Faculty of Science, Srinakharinwirot University, Bangkok 10110, Thailand

Keywords:

Leibniz algebra, Derivation, Antiderivation, Biderivation, Algorithm

Abstract

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.