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\v{C}ech cocycles for quantum principal bundles
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In other to study connections and gauge theories on noncommutative spaces it is useful to use the local trivializations of principal bundles. In this note we show how to use noncommutative localization theory to describe a simple version of cocycle data for the bundles on noncommutative schemes with Hopf algebras in the role of the structure group which locally look like Hopf algebraic smash products. We also show how to use these \v{C}ech cocycles for associated vector bundles. We sketch briefly some examples related to quantum groups.
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Categorified structures over moduli spaces: Anomalies, non-invertible symmetries, and exceptional holonomy
The paper conjectures that non-invertible Ising and tricritical Ising symmetries organize closed string states and D-brane categories into categorical bundles over moduli spaces of exceptional holonomy compactifications.
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