Connes-Moscovici-Kreimer Hopf Algebras

TL;DR

This paper clarifies the mathematical structures underlying Connes-Moscovici and Connes-Kreimer Hopf algebras, highlighting their common features and introducing a new branch related to Feynman-graph Hopf algebras.

Contribution

It isolates shared mathematical aspects of these Hopf algebras and introduces a new branch involving Feynman-graph structures within Hopf algebra theory.

Findings

Identification of common features in Connes-Moscovici and Connes-Kreimer algebras

Introduction of a new branch of Hopf algebras based on Feynman graphs

Discussion of the dual Milnor-Moore situation in this context

Abstract

These notes hopefully provide an aid to the comprehension of the Connes-Moscovici and Connes-Kreimer works, by isolating common mathematical features of the Connes-Moscovici, rooted trees, and Feynman-graph Hopf algebras (as a new special branch of the theory of Hopf algebras expected to become important). We discuss in particular the dual Milnor-Moore situation.