Large scale molecular dynamics simulations are performed to study the steady state yielding dynamics of a well established simple glass. In contrast to the supercooled state, where the shear stress, $σ$, tends to zero at vanishing shear rate, $\gammadot$, a stress plateau forms in the glass which extends over about two decades in shear rate. This strongly suggests the existence of a finite dynamic yield stress in the glass, $σ^+ (T) \equiv σ(T; \gammadot \to 0) >0$. Furthermore, the temperature dependence of $σ^+$ suggests a yield stress discontinuity at the glass transition in agreement with recent theoretical predictions. We scrutinize and support this observation by testing explicitly for the assumptions (affine flow, absence of flow induced ordering) inherent in the theory. Also, a qualitative change of the flow curves enables us to bracket the glass transition temperature $T_c$ of the theory from above and (for the first time in simulations) {\it from below}. Furthermore, the structural relaxation time in the steady state behaves quite similar to the system viscosity at all studied shear rates and temperatures.

4 pages, 5 figures