Jiang-Su Algebra as a Fra\"iss\'e Limit

TL;DR

This paper demonstrates that the Jiang-Su algebra can be constructed as a Fra"iss"e limit of dimension drop algebras, providing an elementary proof and extending the Fra"iss"e framework to UHF algebras.

Contribution

It offers a new elementary proof that the Jiang-Su algebra is a Fra"iss"e limit and shows UHF algebras as Fra"iss"e limits of matrix-valued continuous functions.

Findings

Jiang-Su algebra is a Fra"iss"e limit of dimension drop algebras.

UHF algebras can be realized as Fra"iss"e limits of matrix-valued functions.

Elementary proof simplifies understanding of these C*-algebras as limits.

Abstract

In this paper, we give a self-contained and quite elementary proof that the class of all dimension drop algebras together with their distinguished faithful traces forms a Fra\"iss\'e class with the Jiang-Su algebra as its limit. We also show that the UHF algebras can be realized as Fra\"iss\'e limits of classes of C*-algebras of matrix-valued continuous functions on $[0, 1]$ with faithful traces.