Free brace algebras are free prelie algebras

Details Free brace algebras are free prelie algebras Free brace algebras are free prelie algebras

2008-09-17

arxiv.org/abs/0809.2866v3

Mathematics

Rings and Algebras

10 pages. Final version, to be published in "Communications in Algebra"

Scientific paper

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
Poincar\'e-Hilbert series of g.

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