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Translation map in quantum principal bundles

par Brzezinski, Tomasz
Référence Journal of geometry and physics, 20, 4, page (349-370)
Publication Publié, 1996-11

Article révisé par les pairs

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Résumé :

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.