Lifting right-invariant vector fields and prolongation of connections

W. M. Mikulski

W. M. Mikulski

Annales Polonici Mathematici, Tome 95 (2009), p. 243-252 / Harvested from The Polish Digital Mathematics Library

Résumé

We describe all $_{m} (G)$ -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 $W^{r} P = P^{r} M \times_{M} J^{r} P$ of P → M. In other words, we classify all $_{m} (G)$ -natural transformations $J^{r} L P \times_{M} W^{r} P \to T W^{r} P = L W^{r} P \times_{M} W^{r} P$ covering the identity of $W^{r} P$ , where $J^{r} L P$ is the r-jet prolongation of the Lie algebroid LP=TP/G of P, i.e. we find all $_{m} (G)$ -natural transformations which are similar to the Kumpera-Spencer isomorphism $J^{r} L P = L W^{r} P$ . We formulate axioms which characterize the flow operator of the gauge-bundle $W^{r} P \to M$ . We apply the flow operator to prolongations of connections.

Publié le : 2009-01-01

Zbl 1163.58001

EUDML-ID : urn:eudml:doc:280786

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     title = {Lifting right-invariant vector fields and prolongation of connections},
     journal = {Annales Polonici Mathematici},
     volume = {95},
     year = {2009},
     pages = {243-252},
     zbl = {1163.58001},
     language = {en},
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W. M. Mikulski. Lifting right-invariant vector fields and prolongation of connections. Annales Polonici Mathematici, Tome 95 (2009) pp. 243-252. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap95-3-4/