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Article Dans Une Revue Journal of Geometry and Physics Année : 2023

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

Résumé

In this paper, we present a framework to construct sequences of spectral triples on top of an inductive sequence defining an $AF$-algebra. The 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.

Dates et versions

hal-03720917 , version 1 (12-07-2022)

Identifiants

Citer

Thierry Masson, Gaston Nieuviarts. Lifting Bratteli Diagrams between Krajewski Diagrams: Spectral Triples, Spectral Actions, and $AF$ algebras. Journal of Geometry and Physics, 2023, 187, pp.104784. ⟨10.1016/j.geomphys.2023.104784⟩. ⟨hal-03720917⟩
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