Gauge transformations on quantum principal bundles are extended to differential forms, giving an action on connections and curvature, with the noncommutative 2-torus as the main new example.
On the Durdevic approach to quantum principal bundles
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abstract
We revisit and extend the Durdevic theory of complete calculi on quantum principal bundles. In this setting one naturally obtains a graded Hopf-Galois extension of the higher order calculus and an intrinsic decomposition of degree 1-forms into horizontal and vertical forms. This proposal is appealing, since it is consistently equipped with a canonical braiding and exactness of the Atiyah sequence is guaranteed. Moreover, we provide examples of complete calculi, including the noncommutative 2-torus, the quantum Hopf fibration and differential calculi on crossed product algebras.
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Gauge transformations on quantum principal bundles
Gauge transformations on quantum principal bundles are extended to differential forms, giving an action on connections and curvature, with the noncommutative 2-torus as the main new example.