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ON A GENERALIZED FRAÏSSÉ LIMIT CONSTRUCTION AND ITS APPLICATION TO THE JIANG–SU ALGEBRA

Part of: Linear spaces and algebras of operators Model theory

Published online by Cambridge University Press:  23 October 2020

SHUHEI MASUMOTO
SHUHEI MASUMOTO*
Affiliation:
DEPARTMENT OF GENERAL EDUCATION NATIONAL INSTITUTE OF TECHNOLOGY (KOSEN), KAGAWA COLLEGE 551 KOHDA, TAKUMA-CHO, MITOYO, KAGAWA, JAPANE-mail: masumoto-s@dg.kagawa-nct.ac.jp
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Abstract

In this paper, we present a version of Fraïssé theory for categories of metric structures. Using this version, we show that every UHF algebra can be recognized as a Fraïssé limit of a class of C*-algebras of matrix-valued continuous functions on cubes with distinguished traces. We also give an alternative proof of the fact that the Jiang–Su algebra is the unique simple monotracial C*-algebra among all the inductive limits of prime dimension drop algebras.

Keywords

Fraïssé theoryJiang–Su algebraUHF algebras

MSC classification

Primary: 03C30: Other model constructions
Secondary: 03C98: Applications of model theory 47L40: Limit algebras, subalgebras of $C^*$-algebras
Type
Articles
Information
The Journal of Symbolic Logic , Volume 85 , Issue 3 , September 2020 , pp. 1186 - 1223
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Copyright
© The Association for Symbolic Logic 2020

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References

REFERENCES

Yaacov, I. Ben, Fraïssé limits of metric structures , this Journal, vol. 80 (2015), no. 1, pp. 100–115.Google Scholar
Davidson, K. R., C*- Algebras by Example , Fields Institute Monographs, vol. 6, American Mathematical Society, Providence, RI, 1996, pp. 86–91 Google Scholar
Eagle, C. J., Farah, I., Hart, B., Kadets, B., Kalashnyk, V., and Lupini, M., Fraïssé limits of C*-algebras . this Journal, vol. 81 (2016), no. 2, pp. 755–773.Google Scholar
Elliott, G. and Toms, A., Regularity properties in the classification program for separable amenable C*-algebras . Bulletin of the American Mathematical Society , vol. 45 (2008), no. 2, pp. 229–245.CrossRefGoogle Scholar
Fraïssé, R., Sur l’extension aux relations de quelques propriétés des ordres . Annales Scientifiques de l’École Normale Supérieure , vol. 71 (1954), no. 4, pp. 363–388.CrossRefGoogle Scholar
Hilbert, D., Über die stetige Abbildung einer Linie auf ein Flächenstück . Mathematische Annalen , vol. 38 (1891), no. 3, pp. 459–460.CrossRefGoogle Scholar
Jiang, X. and Su, H., On a simple unital projectionless C*-algebra . American Journal of Mathematics , vol. 121 (1999), no. 2, pp. 359–413.Google Scholar
Lin, H., Approximately diagonalizing matrices over C(Y). Proceedings of the National Academy of Sciences of the United States of America , vol. 109 (2012), no. 8, pp. 2842–2847.CrossRefGoogle Scholar
Masumoto, S., The Jiang–Su algebra as a Fraïssé limit , this Journal, vol. 82 (2017), no. 4, pp. 1541–1559.Google Scholar