Algèbres de greffes

Abstract

In order to study some sets of probabilities, called induced averages by J. Ecalle, F. Menous introduces two grafting operators $B^{+}$ and $B^{-}$. With these two operators, we construct Hopf algebras of rooted and ordered trees ${\mathcal{B}}^i$, $i\in {\mathbb{N}}^{\ast }$, ${\mathcal{B}}^{\infty }$ and $\mathcal{B}$ satisfying the inclusion relations $ \mathcal{B}^{1} \subseteq \hdots \mathcal{B}^{i} \subseteq \mathcal{B}^{i+1} \subseteq \hdots \subseteq \mathcal{B}^{\infty} \subseteq \mathcal{B} $. We endow $\mathcal{B}$ with a structure of duplicial dendriform bialgebra and we deduce that $\mathcal{B}$ is cofree and self-dual. Finally, we introduce the notion of bigraft algebra and we prove that $\mathcal{B}$ is generated as bigraft algebra by the element $ \tdun{1} $.

In french, 32pages

Cited by in corpus (2)

• Mould calculus, polyhedral cones, and characters of combinatorial Hopf algebras
• The bigraft algebras