  In this work, we study the perturbative generation of the gauge invariant
effective action for the non-Abelian gauge field in a $(2+1)$-dimensional
spacetime. We present a detailed analysis of the two, three and four-point
functions in order to determine the non-Abelian Chern-Simons terms (parity odd)
and Yang-Mills terms (parity even). Moreover, these terms are supplemented by
the higher-derivative corrections which resulted in the Alekseev-Arbuzov-Baikov
effective action (parity even) plus the higher-derivative (HD) corrections to
the Chern-Simons terms (parity odd). In order to highlight some features about
the perturbative generation of the effective action, we present a discussion
based on the dimensional analysis, which allows us to establish the general
structure of the permissible terms to guarantee the gauge invariance of the
higher-derivative parts.
