The renormalisation bialgebra and operads

Abstract

In a recent preprint, Brouder and Schmitt give a careful construction of a `renormalisation' Hopf algebra out of an arbitrary bialgebra. In this note, we point out that this is a special case of the construction of the cooperad of a bialgebra (Berger-Moerdijk) combined with the construction of a bialgebra from a cooperad (Frabetti-Van der Laan).

2 pages

Cited by in corpus (2)

• Operads and the Hopf algebras of renormalisation
• On Spineless Cacti, Deligne's Conjecture and Connes--Kreimer's Hopf Algebra