2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/230346We find a Lax pair equation corresponding to the Connes-Kreimer Birkhoff factorization of the character group of a Hopf algebra. This flow preserves the locality of counterterms. In particular, we obtain a flow for the character given by Feynman rules, and relate this flow to the Renormalization Group Flow.Rewritten and expanded version of math-ph/0611014Mathematical PhysicsHigh Energy Physics - Theory81T15, 17B80text