 e., a diffeomorphism "P" × "G" → "P".The existence of the global right action of the structure group picks out a special class of right invariant geometric objects on "P"—those which do not change when they are pulled back along "Rg" for all values of "g" in "G".The most important right invariant objects on a principal bundle are the right invariant vector fields, which form an ideal formula_75 of the Lie algebra of infinitesimal diffeomorphisms on "P".