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| Format: | Preprint |
| Published: |
2025
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| Online Access: | https://arxiv.org/abs/2509.02263 |
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| _version_ | 1866918365012951040 |
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| author | Wagner, Stefan |
| author_facet | Wagner, Stefan |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_02263 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Noncommutative principal bundles and central extensions Wagner, Stefan Operator Algebras Mathematical Physics Rings and Algebras 58B34, 46L85, Secondary 55R10, 16D70 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. |
| title | Noncommutative principal bundles and central extensions |
| topic | Operator Algebras Mathematical Physics Rings and Algebras 58B34, 46L85, Secondary 55R10, 16D70 |
| url | https://arxiv.org/abs/2509.02263 |