Isogroups of differential ideals of vector-valued differential forms: Application to partial differential equations

An older geometric technique for the study of invariance groups of partial differential equations, originally proposed by one of the authors and F. B. Estabrook, is generalized and extended to problems involving exterior equations for vector-valued or Lie algebra-valued exterior differential forms. Use of the method is demonstrated in the study of the symmetry groups of the two-dimensional Dirac equation and the full Yang-Mills free-field equations in Minkowski spacetime.