Classification of generalized symmetries of the Yang–Mills fields with a semi-simple structure group

A complete classification of generalized (or local) symmetries of the Yang–Mills equations on four dimensional Minkowski space with a semisimple structure group is carried out. It is shown that any generalized symmetry, up to a generalized gauge symmetry, agrees with a first order symmetry on solutions of the Yang–Mills equations. Let g=g1+...+gn be the decomposition of the Lie algebra Image of the structure group into simple ideals. First order symmetries for gvalued Yang–Mills fields are found to consist of gauge symmetries, conformal symmetries for gm-valued Yang–Mills fields, 1(less-than-orequals)m(less-than-or-equals), n, and their images under a complex structure of gm.