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arXiv · 0809.2866

Free brace algebras are free prelie algebras

Loïc Foissy
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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.

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Loïc Foissy. 2009-06-23. Free brace algebras are free prelie algebras. https://arxiv.org/abs/0809.2866

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