Noncommutative principal bundles and central extensions

2025/09/02 by Stefan Wagner, Wagner, Stefan
Mathematics · #16D70 #46L55 #47L65 #Advanced Operator Algebra Research #Algebraic structures and combinatorial models #FOS: Mathematics #FOS: Physical sciences #Homotopy and Cohomology in Algebraic Topology #Mathematical Physics (math-ph) #Operator Algebras (math.OA) #Primary 46L85 #Rings and Algebras (math.RA) #Secondary 55R10

paper · pdf · doi:10.48550/arxiv.2509.02263

openalex publication_date 2025/09/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31

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.

Citations

• Collapse in Noncommutative Geometry and Spectral Continuity
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Related

• A Geometric Approach to Noncommutative Principal Bundles
• C*-bundle dynamical systems
• The noncommutative geometry of frame bundles
• Noncommutative Geometry Approach to Principal and Associated Bundles
• On Noncommutative Principal Bundles with Finite Abelian Structure Group