A note on nonidentical Lie relators, Journal of Algebra, 211 (1999), 15--25.

Abstract:

It has been an open question for many years whether the associated Lie ring of a relatively free group is necessarily relatively free (see, for example, [15]). We answer this question in the negative by proving that the variety $B_4B_2$ has Lie relators which are not identical Lie relators