Free brace algebras are free prelie algebras
Lo\"ic Foissy (LM-Reims)
TL;DR
The paper proves that free brace algebras are also free prelie algebras, expanding understanding of their algebraic structure through combinatorial and series manipulations.
Contribution
It demonstrates that free brace algebras are additionally free prelie algebras, providing a new structural insight using planar rooted trees and series analysis.
Findings
Free brace algebras are also free prelie algebras.
The proof uses combinatorial descriptions with planar rooted trees.
Series manipulations confirm the algebraic freeness.
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 Poincar\'e-Hilbert series of g.
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