Free brace algebras are free prelie algebras

Loïc Foissy (1)

1 LMR - Laboratoire de Mathématiques de Reims

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.

Mots clés: Brace algebras; prelie algebras; planar rooted trees

Domaines: Anneaux et algèbres [math.RA]

Loïc Foissy. Free brace algebras are free prelie algebras. Communications in Algebra, 2010. ⟨hal-00322214v3⟩