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arXiv · 2509.02263

Noncommutative principal bundles and central extensions

Stefan Wagner
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Abstract

Motivated by the classical theory of spin structures, we develop a theory for lifting free C$^*$-dynamical systems, a.k.a. noncommutative principal bundles, along central extensions. This theory extends the bundle-theoretic notion of spin structures and yields a complete existence and classification result for such lifts. Using factor system techniques and Picard formalism, our approach introduces new invariants and obstruction classes, thereby unifying geometric, cohomological, and operator-algebraic perspectives. A range of examples demonstrates the scope of the theory.

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Stefan Wagner. 2025-09-02. Noncommutative principal bundles and central extensions. https://arxiv.org/abs/2509.02263

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