Compact Lie algebras do not admit constant Yang-Mills potentials

Considering constant gauge potentials over a Euclidean or Lorentzian n-dimensional vector space with values in some compact Lie algebra the Yang-Mills equations force the gauge field to be Abelian. This theorem is proved and applied to the classical Lie algebras as well as to the exceptional compact Lie algebras. Two examples are given. It is concluded that non-Abelian constant Yang-Mills potentials exist if nilpotent Lie algebras are permitted