∆-PRIMITIVE ELEMENTS OF FREE METABELIAN LIE ALGEBRAS

Let L2be a free metabelian Lie algebra of rank two. We obtaina characterization of ∆-primitive elements of L2. In particular, we prove thatevery endomorphism Φ of L2is an automorhism if and only if Φ takes a ∆primitive element of L2to another ∆-primitive element. Also we show that ina free metabelian Lie algebra of odd rank there are no ∆-primitive elements

Keywords:

Primitive element, Free metabelian Lie algebra,

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Department of Mathematics, C¸ ukurova University , Adana-TURKEY E-mail address: dilekah@cu.edu.tr, ezerrin@cu.edu.tr