ORBITS AND TEST ELEMENTS IN FREE LEIBNIZ ALGEBRAS OF RANK TWO

摘要

Let F be the free Leibniz algebra of rank two over a field K of characteristic zero freely generated by x(1) and x(2). In this article we show that an endomorphism of F which preserves the orbit of a nontrivial element of F is an automorphism. Using this result, we determine some test elements of F.