Lifting Bratteli Diagrams between Krajewski Diagrams: Spectral Triples, Spectral Actions, and algebras
arXiv:2207.04466 · doi:10.1016/j.geomphys.2023.104784
Abstract
In this paper, we present a framework to construct sequences of spectral triples on top of an inductive sequence defining an -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.
28 pages, 2 figures, new version published in Journal of Geometry and Physics