Geodesic
Outer endomorphisms of free metabelian Lie algebras
Serdica Mathematical Journal, Tome 37 (2011) no. 3, pp. 261-276.

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Let Fm be the free metabelian Lie algebra of rank m over a field K of characteristic 0. We consider the semigroup IE(Fm) of the endomorphisms of Fm which are identical modulo the commutator ideal of Fm. We describe the factor semigroup of IE(Fm) modulo the congruence induced by the group of inner automorphisms.
Keywords: Free Metabelian Lie Algebras, Inner Automorphisms, Outer Endomorphisms 
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     title = {Outer endomorphisms of free metabelian {Lie} algebras},
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Findik, Sehmus. Outer endomorphisms of free metabelian Lie algebras. Serdica Mathematical Journal, Tome 37 (2011) no. 3, pp. 261-276. http://geodesic.mathdoc.fr/item/SMJ2_2011_37_3_a6/