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Journal Articles Communications in Algebra Year : 2010

Free brace algebras are free prelie algebras

Loïc Foissy

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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Dates and versions

hal-00322214 , version 1 (17-09-2008)
hal-00322214 , version 2 (26-01-2009)
hal-00322214 , version 3 (23-06-2009)

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

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