  Perturbative quantization of Yang-Mills theory with a gauge algebra given by
the classical double of a semisimple Lie algebra is considered. The classical
double of a real Lie algebra is a nonsemisimple real Lie algebra that admits a
nonpositive definite invariant metric, the indefiniteness of the metric
suggesting an apparent lack of unitarity. It is shown that the theory is UV
divergent at one loop and that there are no radiative corrections at higher
loops. One-loop UV divergences are removed through renormalization of the
coupling constant, thus introducing a renormalization scale. The terms in the
classical action that would spoil unitarity are proved to be cohomologically
trivial with respect to the Slavnov-Taylor operator that controls gauge
invariance for the quantum theory. Hence they do not contribute gauge invariant
radiative corrections to the quantum effective action and the theory is
unitary.
