Spectral triples on the Jiang-Su algebra

TL;DR

This paper constructs spectral triples on specific inductive limit algebras, including the Jiang-Su algebra, using an AF-embedding, advancing the understanding of noncommutative geometric structures.

Contribution

It introduces a method to build spectral triples on inductive limit algebras, notably applying an AF-embedding to the Jiang-Su algebra for the first time.

Findings

Spectral triples successfully constructed on the Jiang-Su algebra.

Method applicable to a class of inductive limit matrix-valued function algebras.

Enhances the framework of noncommutative geometry for complex algebraic structures.

Abstract

We construct spectral triples on a class of particular inductive limits of matrix-valued function algebras. In the special case of the Jiang-Su algebra we employ a particular $AF$-embedding.