Lifting Bratteli diagrams between Krajewski diagrams: Spectral triples, spectral actions, and AF algebras
Abstract
In this paper, we present a framework to construct sequences of spectral triples on top of an inductive sequence defining an AFalgebra. One aim of this paper is to lift arrows of a Bratteli diagram to arrows between Krajewski diagrams. The spectral actions defining Noncommutative 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 derivationbased differential calculus, but the present paper focuses more on the mathematical structure without trying to study the physical implications.
 Publication:

Journal of Geometry and Physics
 Pub Date:
 May 2023
 DOI:
 10.1016/j.geomphys.2023.104784
 arXiv:
 arXiv:2207.04466
 Bibcode:
 2023JGP...18704784M
 Keywords:

 58B34;
 81T75;
 46L87;
 70S15;
 Mathematical Physics;
 High Energy Physics  Theory
 EPrint:
 28 pages, 2 figures, new version published in Journal of Geometry and Physics