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The Local Product Structure of Expansive Automorphisms of Solenoids and Their Associated C*-Algebras

Published online by Cambridge University Press:  20 November 2018

Berndt Brenken
Berndt Brenken*
Affiliation:
Department of Mathematics and Statistics The University of Calgary 2500 University Drive NW Calgary, Alberta T2N1N4
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Abstract

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An explicit description of a hyperbolic canonical coordinate system for an expansive automorphism of a compact connected abelian group is given. These dynamical systems are factors of subshifts of finite type. Some properties of the associated crossed product C*-algebra are discussed. In these examples, the C* -algebras of Ruelle are crossed product algebras.

Keywords

22D4022D4546LXX54H2028D20
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 48 , Issue 4 , 01 August 1996 , pp. 692 - 709
Copyright
Copyright © Canadian Mathematical Society 1996

References

1. Atkin, E., The General Topology of Dynamical Systems, Graduate Studies in Math. 1, Amer. Math. Soc, 1991.Google Scholar
2. Blackadar, B., Dadarlat, M. and Rørdam, M., The real rank of inductive limit C*-algebras, Math., Scand. 69(1991), 211–216.Google Scholar
3. Brenken, B., K-groups of solenoidal algebras 1, Proc. Amer. Math. Soc. (5)23(1995), 1457–1464.Google Scholar
4. Brenken, B., Isomorphism classes of solenoidal algebras 1, Canad. Math. Bull., (4) 36(1993), 414–418.Google Scholar
5. Brenken, B. and Jorgensen, P., A family of dilation crossed product algebras, J. Operator, Theory 25(1991), 299–308.Google Scholar
6. Denker, M., Grillenberger, C. and Sigmund, K., Ergodic theory on compact spaces, Springer Lecture Notes in Math. 527, 1976.Google Scholar
7. Elliott, G., Are amenable C -algebras classifiable?, Contemp., Math. 145(1993), 42S-427.Google Scholar
8. Fried, D., Finitely presented dynamical systems, Ergodic Theory Dynamical, Systems 7(1987), 489–507.Google Scholar
9. Hewitt, E. and Ross, K.A., Abstract Harmonic Analysis, Vol. 1, Springer-Verlag, 1963.Google Scholar
10. Kawamura, S., Tomiyama, J. and Watatani, Y., Finite dimensional irreducible representations of C*- algebras associated with topological dynamical systems, Math., Scand. 56(1985), 241–248.Google Scholar
11. Kitchens, B. and Schmidt, K., Automorphisms of compact groups, Ergodic Theory Dynamical, Systems, 9(1989), 691–735.Google Scholar
12. Lam, P.F., On expansive automorphism transformation groups, Trans. Amer. Math., Soc. 105(1970), 131–138.Google Scholar
13. Lawton, W., The structure of compact connected groups which admit an expansive automorphism, Springer Lecture Notes in, Math. 318(1973), 182–196.Google Scholar
14. Laxton, R. and Parry, W., On the periodic points of certain automorphisms and a system of polynomial identities, J., Algebra 6(1967), 388–393.Google Scholar
15. Lind, D., Schmidt, K. and Ward, T., Mahler Measure and Entropy for Commuting Automorphisms of Compact Groups, Invent. Math., (3) 101(1990), 593–629.Google Scholar
16. Lind, D. and Ward, T., Automorphisms of solenoids and p-adic entropy, Ergodic Theory Dynamical, Systems 8(1988), 411-119.Google Scholar
17. Putnam, I., C-algebras from Smale spaces, preprint.Google Scholar
18. Rjardam, M., Classification of certain infinite simple C-algebras, J. Funct. Anal., to appear.Google Scholar
19. Ruelle, D., Noncommutative algebras for hyperbolic diffeomorphisms, Invent., Math. 93(1988), 1–13.Google Scholar
20. Ruelle, D., Thermodynamic Formalism, Encyclopedia of Math. Appl. 5, Addison-Wesley, Reading, 1978.Google Scholar
21. Steenrod, N., The Topology of Fibre Bundles, Princeton University Press, Princeton, 1951.Google Scholar
22. Spanier, E., Algebraic Topology, McGraw-Hill, New York, 1966.Google Scholar
23. Walters, P., An Introduction to Ergodic Theory, Graduate Texts in Math., Springer-Verlag, 1982.Google Scholar