Subject: question for the toplist From: "A Lazarev, Mathematics" Date: Wed, 06 Oct 2004 19:35:24 +0100 Let k be a commutative ring of char 0 and L be a nilpotent graded Lie algebra over k, free and of finite rank as a k-module. Let UL be the COMPLETED universal enveloping algebra of L by which I mean inverse lim(UL/I^n) where I is the augmentation ideal of UL. Then is it true that the canonical map L-->UL is injective? Note that in his paper 'Rational homotopy theory' Quillen has a corresponding statement for an ungraded Lie algebra and under the assumption that k be a field. In addition, it is not hard to prove the statement I need if L is a free Lie algebra (admittedly, nonnilpotent, but close). Regards, Andrey ---------------------- A Lazarev, Mathematics A.Lazarev@bristol.ac.uk