2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/56773These 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.Proceedings of the conference on``Mathematical Physics and in Mathematics and Physics'', Siena, 20-25 June 2000Mathematical Physicstext