On a generalized Fra\"iss\'e limit construction

TL;DR

This paper introduces a modified Fra"iss"e theory framework and demonstrates that UHF algebras can be characterized as Fra"iss"e limits of specific classes of C*-algebras, expanding the applicability of Fra"iss"e theory.

Contribution

The paper presents a generalized Fra"iss"e limit construction and applies it to identify UHF algebras as limits of matrix-valued continuous functions on cubes.

Findings

UHF algebras can be realized as Fra"iss"e limits.

A modified Fra"iss"e theory framework is developed.

Application to C*-algebras of matrix-valued functions.

Abstract

In this paper, we present a slightly modified version of Fra\"iss\'e theory which is used in a paper by Christopher J. Eagle, Ilijas Farah, Bradd Hart, Boris Kadets, Vladyslav Kalashnyk and Martino Lupini (arXiv:1411.4066) and another by the author (arXiv:1602.00124). Using this version, we also show that every UHF algebra can be recognized as a Fra\"iss\'e limit of a class of C*-algebras of matrix-valued continuous functions on cubes with distinguished traces.