Endomorphisms which preserve orbits of free metabelian Leibniz algebras.

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 ∈ M ′ is an automorphism. Additionally, we give some test elements. [ABSTRACT FROM AUTHOR]