Hostname: page-component-78c5997874-fbnjt Total loading time: 0 Render date: 2024-11-20T00:38:49.405Z Has data issue: false hasContentIssue false
  • English
  • Français

THE JIANG–SU ALGEBRA AS A FRAÏSSÉ LIMIT

Published online by Cambridge University Press:  16 May 2017

SHUHEI MASUMOTO
SHUHEI MASUMOTO*
Affiliation:
GRADUATE SCHOOL OF MATHEMATICAL SCIENCETHE UNIVERSITY OF TOKYO3-8-1 KOMABA, MEGURO-KU TOKYO 153-8914, JAPANE-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

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 Fraïssé class with the Jiang–Su algebra as its limit. We also show that the UHF algebras can be realized as Fraïssé limits of classes of C*-algebras of matrix-valued continuous functions on [0,1] with faithful traces.

Keywords

Primary 47L40Secondary 03C98Fraïssé theoryJiang–Su algebraUHF algebra
Type
Articles
Information
The Journal of Symbolic Logic , Volume 82 , Issue 4 , December 2017 , pp. 1541 - 1559
Copyright
Copyright © The Association for Symbolic Logic 2017 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Ben Yaacov, I., 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.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. A. and Tom, A. S., 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.Google Scholar
Fraïssé, R., Sur l’extension aux relations de quelques propriétés des ordres . Annales Scientifiques de l’École Normale Supérieure, Sér. 3, vol. 71 (1954), no. 4, pp. 363–388.Google Scholar
Glimm, J. G., On a certain class of C*-algebras . Transactions of the American Mathematical Society, vol. 95 (1960), pp. 318–340.Google 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.CrossRefGoogle Scholar
Kubiś, W. and Solecki, S., A proof of the uniqueness of the Gurariĭ space . Israel Journal of Mathematics, vol. 195 (2013), no. 1, pp. 449–456.Google Scholar
Lupini, M., Uniqueness, universality, and homogeneity of the noncommutative Gurarij space . Advances in Mathematics, vol. 298 (2016), pp. 286–324.Google Scholar
Rørdam, M., Lausen, F., and Laustsen, N., An Introduction to K-theory for C*-algebras, London Mathematical Society Student Texts, vol. 49, Cambridge University Press, Cambridge, 2000.Google Scholar
Schoretsanitis, K., Fraïssé theory for metric structures, Ph.D. thesis, the Graduate College of the University of Illinois at Urbana-Champaign, 2007.Google Scholar