Translation Map in Quantum Principal Bundles
نویسنده
چکیده
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 → 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 AdR-covariant maps A → P . Current address: Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge CB3 9EW, U.K. E-mail: [email protected]
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