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

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.