Hostname: page-component-848d4c4894-2xdlg Total loading time: 0 Render date: 2024-07-05T20:48:47.640Z Has data issue: false hasContentIssue false
  • English
  • Français

C*-algebras arising from substitutions

Published online by Cambridge University Press:  24 November 2009

MASARU FUJINO
MASARU FUJINO*
Affiliation:
Graduate School of Mathematics, Kyushu University, Hakozaki, Fukuoka, 812-8581, Japan (email: fujino@math.kyushu-u.ac.jp)
Get access Rights & Permissions [Opens in a new window]

Abstract

In this paper, we introduce a C*-algebra associated with a primitive substitution. We show that when σ is proper, the C*-algebra is simple and purely infinite and contains the associated Cuntz–Krieger algebra and the crossed product C*-algebra of the corresponding Cantor minimal system. We calculate the K-groups.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 30 , Issue 6 , December 2010 , pp. 1685 - 1702
Copyright
Copyright © Cambridge University Press 2009

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

[1]Cuntz, J.. Simple C *-algebras generated by isometries. Comm. Math. Phys. 57 (1977), 173–185.CrossRefGoogle Scholar
[2]Cuntz, J.. C *-algebras associated with the ax+b-semigroup over ℕ. K-theory and Noncommutative Geometry (Valladolid, 2006). European Mathematical Society, 2008, pp. 201–215.CrossRefGoogle Scholar
[3]Cuntz, J. and Krieger, W.. A class of C *-algebras and topological Markov chains. Invent. Math. 56 (1980), 251–268.CrossRefGoogle Scholar
[4]Davidson, K. R.. C *-Algebras by Example (Fields Institute Monographs, 6). American Mathematical Society, Providence, RI, 1996.CrossRefGoogle Scholar
[5]Durand, F., Host, B. and Skau, C. F.. Substitutional dynamical systems, Bratteli diagrams and dimension groups. Ergod. Th. & Dynam. Sys. 19 (1999), 953–993.CrossRefGoogle Scholar
[6]Giordano, T., Putnam, I. F. and Skau, C. F.. Topological orbit equivalence and C *-crossed product. J. Reine Angew. Math. 469 (1995), 51–111.Google Scholar
[7]Herman, R. H., Putnam, I. P. and Skau, C. F.. Ordered Bratteli diagrams, dimension groups, and topological dynamics. Int. J. Math. 3 (1992), 827–864.CrossRefGoogle Scholar
[8]Host, B.. Substitution subshifts and Bratteli diagrams. Topics in Symbolic Dynamics and Applications (London Mathematical Society Lecture Note Series, 279). Eds. Blanchard, F., Maass, A. and Nogueira, A.. Cambridge University Press, Cambridge, 1999.Google Scholar
[9]Pimsner, M. and Voiculescu, D. V.. K-groups of reduced crossed products by free groups. J. Operator Theory 4 (1982), 131–156.Google Scholar
[10]Queffelec, M.. Substitution Dynamical Systems (Lecture Notes in Mathematics, 1924). Springer, Berlin, 1987.Google Scholar
[11]Rørdam, M.. Classification of certain infinite simple C *-algebras. J. Funct. Anal. 131 (1995), 415–458.CrossRefGoogle Scholar