Free brace algebras are free prelie algebras
arXiv:0809.2866
Abstract
Let g be a free brace algebra. This structure implies that g is also a prelie algebra and a Lie algebra. It is already known that g is a free Lie algebra. We prove here that g is also a free prelie algebra, using a description of g with the help of planar rooted trees, a permutative product, and anipulations on the Poincaré-Hilbert series of g.
10 pages. Final version, to be published in "Communications in Algebra"