Lifting right-invariant vector fields and prolongation of connections

• Autorzy: W. M. Mikulski
• Języki publikacji: EN

Abstrakty

EN

We describe all $𝓟𝓑_m(G)$-gauge-natural operators 𝓐 lifting right-invariant vector fields X on principal G-bundles P → M with m-dimensional bases into vector fields 𝓐(X) on the rth order principal prolongation $W^rP=P^rM×_MJ^rP$ of P → M. In other words, we classify all $𝓟𝓑_m(G)$-natural transformations $J^rLP×_M W^rP→ TW^rP=LW^rP×_MW^rP$ covering the identity of $W^rP$, where $J^rLP$ is the r-jet prolongation of the Lie algebroid LP=TP/G of P, i.e. we find all $𝓟𝓑_m(G)$-natural transformations which are similar to the Kumpera-Spencer isomorphism $J^rLP=LW^rP$. We formulate axioms which characterize the flow operator of the gauge-bundle $W^rP → M$. We apply the flow operator to prolongations of connections.

Kategorie tematyczne

• 58A32: Natural bundles
• 58A20: Jets

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 2009
• Tom: 95
• Numer: 3
• Strony: 243-252

Daty

wydano

2009

Twórcy

autor

W. M. Mikulski

• Institute of Mathematics, Jagiellonian University, Łojasiewicza 6, 30-348 Kraków, Poland

Identyfikatory

DOI

10.4064/ap95-3-4