On inductive limit spectral triples

TL;DR

This paper investigates conditions for constructing spectral triples as inductive limits of simpler triples, providing a framework to analyze classical examples within this context.

Contribution

It establishes criteria under which inductive limits of spectral triples form valid spectral triples and applies these to classical examples.

Findings

Derived conditions for inductive limit spectral triples

Analyzed classical spectral triples using these conditions

Provided a framework for constructing spectral triples as limits

Abstract

Given an inductive system of spectral triples $\{(A_j,\H_j,D_j)\}_j$, we find conditions under which the triple $(\limind A_j,\limind H_j,\limind D_j)$ is a spectral triple. We also analyze and describe some classical examples of spectral triples in terms of these conditions.