Physique Nucléaire Théorique et Physique Mathématique, Université Libre de Bruxelles, Campus de la Plaine CP 229, B-1050, Brussels, Belgium
Abstract:
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.