On the respective terms of the derived and the polycentral series of a free lie algabra and an ideal
Title:
On the respective terms of the derived and the polycentral series of a free lie algabra and an ideal
Author:
Boral, Melih Soylemez, Hasan
Appeared in:
Communications in algebra
Paging:
Volume 20 (1992) nr. 12 pages 3723-3728
Year:
1992
Contents:
Let F be a free Lie algebra of rank> 1 and S be an ideal of F. Denote by Fm and Fnl,…,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 Fnl,…,nk/Snl,…,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 Fnl…,nk/Snl is infinitely generated.
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