On the Connes-Kreimer construction of Hopf Algebras

TL;DR

This paper presents a universal method to construct families of Hopf P-algebras for any Hopf operad, generalizing the Connes-Kreimer Hopf algebra of rooted trees.

Contribution

It introduces a universal construction framework for Hopf P-algebras applicable to all Hopf operads, extending the Connes-Kreimer algebra.

Findings

Provides a universal construction for Hopf P-algebras

Recovers the Connes-Kreimer Hopf algebra as a special case

Extends the theory of Hopf algebras in operadic contexts

Abstract

We give a universal construction of families of Hopf $P$-algebras for any Hopf operad $P$. As a special case, we recover the Connes-Kreimer Hopf algebra of rooted trees.