Alg\`ebres de greffes
Anthony Mansuy (LM-Reims)

TL;DR
This paper constructs and analyzes a hierarchy of Hopf algebras of rooted trees using grafting operators, revealing their cofree, self-dual structure and generating properties within bigraft algebras.
Contribution
It introduces new grafting operators to build a family of Hopf algebras of rooted trees and studies their algebraic properties and structures.
Findings
The Hopf algebras form an increasing hierarchy with specific inclusion relations.
The algebra is cofree and self-dual.
is generated as a bigraft algebra by a single element.
Abstract
In order to study some sets of probabilities, called induced averages by J. Ecalle, F. Menous introduces two grafting operators and . With these two operators, we construct Hopf algebras of rooted and ordered trees , , and satisfying the inclusion relations . We endow with a structure of duplicial dendriform bialgebra and we deduce that is cofree and self-dual. Finally, we introduce the notion of bigraft algebra and we prove that is generated as bigraft algebra by the element .
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Taxonomy
TopicsAdvanced Topics in Algebra · Algebraic structures and combinatorial models · Homotopy and Cohomology in Algebraic Topology
