PARAFREE METABELIAN LIE ALGEBRAS WHICH ARE DETERMINED BY PARAFREE LIE ALGEBRAS

Abstract

Let L be a Lie algebra. Denote by k(L) the k-th term of thederived series of L and by w(L) the intersection of the ideals I of L suchthat L=I is nilpotent. We prove that if P is a parafree Lie algebra, thenthe algebra Q = (P=k(P))=w(P=k(P)); k 2 is a parafree solvable Liealgebra. Moreover we show that if Q is not free metabelian, then P is not freesolvable for k = 2.