Abstract
Let F be a free Lie algebra of rank> 1 and S be an ideal of F. Denote by Fm and Fn l,…,nk the terms of the lower central and the polycentral series of F. The aim of this paper is to provide a sufficient condition for the quotient algebra Fn l,…,nk/Sn l,…,nk to be infinitely generated. The case Fm/Sm was studied in [6] for free groups and in [ 2 ] for free Lie algebras. In this paper the following main theorem is proved : If F = F2 = S, k > 1 and ni > 1 for i=l,…, k, then Fn l…,nk/Sn l is infinitely generated.
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