Determination of endomorphisms of free metabelian Lie algebras (Q5938489)

Let \(G\) be the free finitely generated metabelian group of rank \(n\). \textit{E.~I.~Timoshenko} [Math. Notes 62, No. 6, 767-770 (1997; Zbl 0615.20055)] found necessary and sufficient conditions on elements of \(G\) for every endomorphism of \(G\) to be uniquely determined from its action on these elements. Let \(M_n\) be the free metabelian Lie algebra with \(n\) generators. In the article under review the authors find necessary and sufficient conditions on elements of \(M_n\) for every endomorphism of \(M_n\) to be uniquely determined from the action on these elements.