2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/196295We study the Connes-Kreimer Hopf algebra of renormalization in the case of gauge theories. We show that the Ward identities and the Slavnov-Taylor identities (in the abelian and non-abelian case respectively) are compatible with the Hopf algebra structure, in that they generate a Hopf ideal. Consequently, the quotient Hopf algebra is well-defined and has those identities built in. This provides a purely combinatorial and rigorous proof of compatibility of the Slavnov-Taylor identities with renormalization.24 pages; uses feynmfHigh Energy Physics - TheoryMathematical Physicstext