Geodesic
C*-Algebras from Smale Spaces
Canadian journal of mathematics, Tome 48 (1996) no. 1, pp. 175-195

Voir la notice de l'article provenant de la source Cambridge University Press

We consider the C*-algebras constructed from certain hyperbolic dynamical systems. The construction, due to Ruelle, generalizes the C*-algebras of Cuntz and Krieger. We discuss relations between the C*-algebras, show the existence of natural asymptotically abelian systems and investigate the K-theory and E-theory of these C*-algebras.
DOI : 10.4153/CJM-1996-008-2
Mots-clés : 46L05, 45L80, 19K14, 58F15 
Putnam, Ian F. C*-Algebras from Smale Spaces. Canadian journal of mathematics, Tome 48 (1996) no. 1, pp. 175-195. doi: 10.4153/CJM-1996-008-2
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[1] 1. Blackadar, B., K-theoryfor Operator Algebras. Mathematical Sciences Research Institute, Publication 5, Springer-Verlag, Berlin, Heidelberg, New York, 1986. Google Scholar

[2] 2. Bowen, R., On Axiom A diffeomorphisms, CBMS Lecture Notes 35, Amer. Math. Soc, Providence, 1978. Google Scholar

[3] 3. Connes, A., A survey of foliations and operator algebras, Operator Algebras and Applications, (ed. Kadison, R.V.), Proc. Symp. Pure Math. 38, Amer. Math. Soc, Providence, 1981. 521–628. Google Scholar

[4] 4. Connes, A., An analogue of the Thorn isomorphism for crossed products of a C*-algebra by an action ofR, Adv. in Math. 39(1981), 31–55. Google Scholar

[5] 5. Connes, A. and Higson, N., Deformations, morphismes asymptotiques et K-théorie bivariant, C. R. Acad. Sci. Séries 1311(1990), 101–106. Google Scholar

[6] 6. Cuntz, J. and Krieger, W., A class of C*-algebras and topological Markov chains, Invent. Math. 56(1980), 251–268. Google Scholar

[7] 7. Handelman, D., Positive matrices and dimension groups affiliated to C* -algebras and topological Markov chains, J. Operator Theory 6(1981), 55–74. Google Scholar

[8] 8. Krieger, W., On dimension functions and topological Markov chains, Invent. Math. 56(1980), 239–250. Google Scholar

[9] 9. Muhly, P.S., Renault, J.N. and Williams, D.P., Equivalence and isomorphism for groupoid C*-algebras, J. Operator Theory 17(1987), 3–22. Google Scholar

[10] 10. Pedersen, G.K., C*-algebras and their automorphism groups. London Math. Soc. Monographs 14, Academic Press, London, 1979. Google Scholar

[11] 11. Renault, J.N., A groupoid approach to C* -algebras. Lecture Notes in Math. 793, Springer-Verlag, Berlin, Heidelberg, New York, 1980. Google Scholar

[12] 12. Rowen, L.H., Ring Theory. Academic Press, London, 1991. Google Scholar

[13] 13. Ruelle, D., Thermodynamic Formalism. Encyclopedia of Math, and its Appl. 5. Massachusetts, Addison- Wesley, Reading, 1978. Google Scholar

[14] 14. Ruelle, D., Noncommutative algebras for hyperbolic diffeomorphisms, Invent. Math. 93(1988), 1—13. Google Scholar

[15] 15. Ruelle, D. and Sullivan, D., Currents, flows and diffeomorphisms, Topology 14(1975), 319–327. Google Scholar

[16] 16. Smale, S., Differentiable dynamical systems, Bull. Amer. Math. Soc. 73(1967), 747–817. Google Scholar

[17] 17. Takai, H., KK-theoryofthe C*-algebra of Anosov foliations. Geometric Methods in Operator Algebras, (ed. Araki, H. and Effros, E.G.), Pitman Res. Notes in Math. 123, Wiley, New York, 1986. Google Scholar

[18] 18. Walters, P., An Introduction to Ergodic Theory. Graduate Texts in Math., Springer-Verlag, Berlin, Heidelberg, New York, 1982. Google Scholar

[19] 19. Williams, R.F., One-dimensional non-wandering sets, Topology 6(1967), 473–487. Google Scholar

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