Orbits and Test Elements in Free Leibniz Algebras of Rank Two: Communications in Algebra: Vol 43, No 8

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Abstract

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.

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Communicated by J.-T. Yu.

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Orbits and Test Elements in Free Leibniz Algebras of Rank Two

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