Invariant Connections in a Non-Abelian Principal Bundle

Abstract Given a transitive action of a symmetry group G on the base space B of a non-Abelian principal bundle P ω with a connection ω, we study the way this action can be lifted to a certain action of G on P ω leaving invariant ω. We show that such an action is described by a two-cocycle of G with values on the group of identity lifts, H l . The general properties of these two-cocycles are investigated and some cases for principal bundles with SU ( n ) as gauge group are worked out.