Lifting right-invariant vector fields and prolongation of connections
W. M. Mikulski (2009)
Annales Polonici Mathematici
Similarity:
We describe all -gauge-natural operators lifting right-invariant vector fields X on principal G-bundles P → M with m-dimensional bases into vector fields (X) on the rth order principal prolongation of P → M. In other words, we classify all -natural transformations covering the identity of , where is the r-jet prolongation of the Lie algebroid LP=TP/G of P, i.e. we find all -natural transformations which are similar to the Kumpera-Spencer isomorphism . We formulate axioms which...