= Solution
Choose Lie-algebra generators with $[T_b,T_c]=f^a{}_{bc}T_a$ and an invariant orthonormal color metric. Since the coupling is placed outside the gauge kinetic term, it is absorbed into $A_\mu$ in the connection convention. The <gauge field strength> and <adjoint covariant derivative> are
$$
\boxed{F_{\mu\nu}^a=\partial_\mu A_\nu^a-\partial_\nu A_\mu^a+f^a{}_{bc}A_\mu^bA_\nu^c,\qquad
(D_\mu c)^a=\partial_\mu c^a+f^a{}_{bc}A_\mu^bc^c.}
$$
The <structure constants> are antisymmetric in $b,c$ and obey the <Jacobi identity>. These definitions give $[D_\mu,D_\nu]v=[F_{\mu\nu},v]$ on an adjoint-valued field. The field $c$ is a Grassmann-odd <Faddeev-Popov ghost field>; the Lie bracket in $D_\mu c$ contracts its color components in the same way as for any adjoint field.
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