Almost Tame Automorphisms of Two Generated Free Leibniz Algebras

Abstract

Denote a free Leibniz algebra in two variables over a field K by LB ⟨ x, y ⟩. The groups of almost triangular AT(LB ⟨ x, y ⟩) and almost tame automorphisms Tame(LB ⟨ x, y ⟩) of LB ⟨ x, y ⟩ are introduced here. These groups extend the groups of triangular and tame automorphisms, respectively. We prove that where H = GL 2(K) ∩ AT(LB ⟨ x, y ⟩). We also show that Tame(LB ⟨ x, y ⟩) is smaller than the group of automorphisms of LB ⟨ x, y ⟩.