Translation map in quantum principal bundles

Details Translation map in quantum principal bundles Translation map in quantum principal bundles

1994-07-22

arxiv.org/abs/hep-th/9407145v2

J.Geom.Phys. 20 (1996) 349

Physics

High Energy Physics

High Energy Physics - Theory

24 pages. Substantial changes in presentation. New section added with an explicitly computed example. To appear in J. Geom. Ph

Scientific paper

10.1016/S0393-0440(96)00003-4

The notion of a translation map in a quantum principal bundle is introduced. A translation map is then used to prove that the cross sections of a quantum fibre bundle $E(B,V,A)$ associated to a quantum principal bundle $P(B,A)$ are in bijective correspondence with equivariant maps $V\to P$, and that a quantum principal bundle is trivial if it admits a cross section which is an algebra map. The vertical automorphisms and gauge transformations of a quantum principal bundle are discussed. In particular it is shown that vertical automorphisms are in bijective correspondence with $\ad$-covariant maps $A\to P$.

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