Fra\"iss\'e limits of C*-algebras
Christopher J. Eagle, Ilijas Farah, Bradd Hart, Boris Kadets, and Vladyslav Kalashnyk, Martino Lupini
TL;DR
This paper applies Fra"issé theory to operator algebras, constructing key algebras as limits of classes of structures and deriving new homogeneous examples and Ramsey-theoretic results.
Contribution
It introduces a novel Fra"issé-theoretic framework for realizing important C*-algebras and hyperfinite factors, providing new homogeneous AF algebra examples.
Findings
Jiang-Su algebra realized as a Fra"issé limit
All UHF algebras constructed via Fra"issé theory
Ramsey-theoretic results for full-matrix algebras
Abstract
We realize the Jiang-Su algebra, all UHF algebras, and the hyperfinite II factor as Fra\"iss\'e limits of suitable classes of structures. Moreover by means of Fra\"iss\'e theory we provide new examples of AF algebras with strong homogeneity properties. As a consequence of our analysis we deduce Ramsey-theoretic results about the class of full-matrix algebras.
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