Endomorphisms which preserve orbits of free metabelian Leibniz algebras

Abstract

Let M be the free metabelian Leibniz algebra of rank two over a field K of characteristic 0. In this article, we show that an endomorphism of M which preserves the orbit of a nontrivial certain kind of element $w\in M^{\prime }$ is an automorphism. Additionally, we give some test elements.

KEYWORDS:

• Automorphism
• free metabelian Leibniz algebras
• orbit
• test element

2020 MATHEMATICS SUBJECT CLASSIFICATION:

• Primary: 17A32
• 17A36
• Secondary: 17A50

Disclosure statement

The authors declare that there are no conflicts of interest