Free ideals of one-relator graded Lie algebras

John P. Labute
1995 Transactions of the American Mathematical Society  
In this paper we show that a one-relator graded Lie algebra g = L/ir), over a principal ideal domain K, has a homogeneous ideal f) with fl/f) a free K-module of finite rank if the relator r is not a proper multiple of another element in the free Lie algebra L . As an application, we deduce that the center of a one-relator Lie algebra over K is trivial if the rank of L is greater than two. As another application, we find a new class of one-relator pro-p-groups which are of cohomological dimension 2.
more » ... omological dimension 2.
doi:10.1090/s0002-9947-1995-1282891-0 fatcat:y2zyawogijcyxnv3tjigtympo4