Lifting Bratteli Diagrams between Krajewski Diagrams: Spectral Triples, Spectral Actions, and $AF$ algebras

Autor: T. Masson, G. Nieuviarts
Přispěvatelé: Centre de Physique Théorique - UMR 7332 (CPT), Aix Marseille Université (AMU)-Université de Toulon (UTLN)-Centre National de la Recherche Scientifique (CNRS), CPT - E2 Géométrie, Physique et Symétries, Aix Marseille Université (AMU)-Université de Toulon (UTLN)-Centre National de la Recherche Scientifique (CNRS)-Aix Marseille Université (AMU)-Université de Toulon (UTLN)-Centre National de la Recherche Scientifique (CNRS)
Rok vydání: 2022
Předmět:
Zdroj: Journal of Geometry and Physics
Journal of Geometry and Physics, 2023, 187, pp.104784. ⟨10.1016/j.geomphys.2023.104784⟩
ISSN: 0393-0440
DOI: 10.48550/arxiv.2207.04466
Popis: In this paper, we present a framework to construct sequences of spectral triples on top of an inductive sequence defining an $AF$-algebra. One aim of this paper is to lift arrows of a Bratteli diagram to arrows between Krajewski diagrams. The spectral actions defining Non-commutative Gauge Field Theories associated to two spectral triples related by these arrows are compared (tensored by a commutative spectral triple to put us in the context of Almost Commutative manifolds). This paper is a follow up of a previous one in which this program was defined and physically illustrated in the framework of the derivation-based differential calculus, but the present paper focuses more on the mathematical structure without trying to study the physical implications.
Comment: 28 pages, 2 figures, new version published in Journal of Geometry and Physics
Databáze: OpenAIRE
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