From Groups to Leibniz Algebras: Common Approaches, Parallel Results

Abstract

In this article, we study (locally) nilpotent and hyper-central Leibniz algebras. We obtained results similar to those in group theory. For instance, we proved a result analogous to the Hirsch-Plotkin Theorem for locally nilpotent groups.

Keywords

• Leibniz algebra
• Lie algebra
• locally nilpotent Leibniz algebra
• hypercentral Leibniz algebra
• Leibniz algebra with the idealizer condition