Self-consistency of off-shell Slavnov-Taylor identities in QCD

Using Hopf-algebraic structures as well as diagrammatic techniques for determining the Slavnov-Taylor identities for QCD we construct the relations for the triple and quartic gluon vertices at one loop. By making the longitudinal projection on an external gluon of a Green's function we show that the gluon self-energy of that leg is consistently replaced by a ghost self-energy. The resulting identities are then studied by evaluating all the graphs for an off-shell nonexceptional momentum configuration. In the case of the 3-point function this is for the most general momentum case and for the 4-point function we consider the fully symmetric point.