Spectral C*-categories and Fell bundles with path-lifting

2013/08/23 by Rachel A. D. Martins, Martins, Rachel A. D. · 1 citation
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Black Holes and Theoretical Physics #FOS: Mathematics #Noncommutative and Quantum Gravity Theories #Operator Algebras (math.OA) #math.OA

paper · pdf · doi:10.48550/arxiv.1308.5247

20 pages, 1 figure

openalex publication_date 2013/08/23 · arxiv created 2014/02/17 · arxiv updated 2014/02/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Following Crane's suggestion that categorification should be of fundamental importance in quantising gravity, we show that finite dimensional even S^o-real spectral triples over \bbc are already nothing more than full C*-categories together with a self-adjoint section of their domain and range maps, while the latter are equivalent to unital saturated Fell bundles over pair groupoids equipped with a path-lifting operator given by a normaliser. Interpretations can be made in the direction of quantum Higgs gravity. These geometries are automatically quantum geometries and we reconstruct the classical limit, that is, general relativity on a Riemannian spin manifold.

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