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A note on the ideals of groupoid C*-algebras from Smale spaces

Published online by Cambridge University Press:  17 April 2009

Chengjun Hou
Affiliation:
Department of mathematics, Qufu Normal University, qufu 273165, Shandong, People's Republic of China, e-mail: chjhou@etang.com
Xiamoman Chen
Affiliation:
Institute of Mathematics Fudan University, Shanghai 200433, People's Republic China, e-mail: xchen@ms.fudan.edu.cn
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In this note, we characterise completely the ideals of the groupoid C*-algebra arising from the asymptotic equivalence relation on the points of a Smale space and show that the related Ruelle algebra is simple when the Smale space is topologically transitive.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 2001

References

[1]Anantharaman-Delaroche, C. and Renault, J., ‘Amenable groupoids’,(preprint).Google Scholar
[2]Fried, D., ‘Métrique naturelles sur les espaces de Smale’, C. R. Acad. Sc. Paris Sér. I 297 (1983), 7779.Google Scholar
[3]Muhly, P.S., Renault, J. and Williams, D., ‘Equivalence and isomorphism for groupoid C*-algebras’, J. Operator Theory 17 (1987), 323.Google Scholar
[4]Putnam, I.F., ‘C*-algebras from Smale spaces’, Canad. J. Math. 48 (1996), 175195.Google Scholar
[5]Putnam, I.F., Hyperbolic systems and generalized Cuntz-Krieger algebras, Lecture Notes from the Summer School in Operator Algebras, 1996 (Odense, Denmark, 1996).Google Scholar
[6]Putnam, I.F. and Spielberg, J., ‘On the structure of C*-algebras associated with hyperbolic dynamical systems’, J. Functional Anal. (to appear).Google Scholar
[7]Renault, J., A groupoid approach to C* algebras, Lecture Notes in Math. 793 (Springer-Verlag, Berlin, Heidelberg, New York, 1980).Google Scholar
[8]Ruelle, D., ‘Noncommuntative algebras for hyperbolic diffeomorphisms’, Invent. Math. 93 (1988), 113.Google Scholar
[9]Ruelle, D., Thermodynamic formalism, Encyclopedia of Math. and its Appl. 5 (Addison-Wesley, Reading, 1978).Google Scholar