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arXiv · hep-th/9407145

Translation map in quantum principal bundles

Tomasz Brzezinski
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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 $V\to P$, 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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Tomasz Brzezinski. 1996-01-11. Translation map in quantum principal bundles. https://doi.org/10.1016/s0393-0440(96)00003-4

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