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We analyze the Chern-Simons-like term generation in the CPT-oddLorentz-violating Yang-Mills theory interacting with fermions. Moreover, westudy the anomalies of this model as well as its quantum stability. The wholeanalysis is performed within the algebraic renormalization theory, which isindependent of the renormalization scheme. In addition, all results are validto all orders in perturbation theory. We find that the Chern-Simons-like termis not generated by radiative corrections, just like its Abelian version.Additionally, the model is also free of gauge anomalies and quantum stable.

Lorentz-violating Yang-Mills theory: discussing the Chern-Simons-like term generation