ON THE RESPECTIVE TERMS OF THE DERIVED AND THE POLYCENTRAL SERIES OF A FREE LIE-ALGEBRA AND AN IDEAL

WOS: A1992KA99800013Let F be a free Lie algebra of rank > 1 and S be an ideal of F. Denote by F(m) and F(n1),...,n(k) 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 F(n1),..,n(k)/S(n1),..n(k) to be infinitely generated. The case F(m)/S(m) 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 not-equal F2 + S, k greater-than-or-equal-to 1 and n(i) > 1 for i=1,..,k, then F(n1),..,n(k)/S(n1),..,n(k) is infinitely generated