On derivations of Leibniz algebras

Abstract

Leibniz algebras are non-antisymmetric generalizations of Lie algebras. In this paper, we investigate the properties of complete Leibniz algebras under certain conditions on their extensions. Additionally, we explore the properties of derivations and direct sums of Leibniz algebras, proving several results analogous to those in Lie algebras.

Keywords

• leibniz algebra
• completeness
• extension
• holomorph
• derivation
• direct sum
• decomposition