Orbits and Test Elements in Free Leibniz Algebras of Rank Two

Author： Özkurt Zeynep  

Publisher： Taylor & Francis Ltd

E-ISSN： 1532-4125|43|8|3534-3544

ISSN： 0092-7872

Source： Communications in Algebra, Vol.43, Iss.8, 2015-08, pp. : 3534-3544

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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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