Hostname: page-component-848d4c4894-tn8tq Total loading time: 0 Render date: 2024-06-26T11:40:46.689Z Has data issue: false hasContentIssue false
  • English
  • Français

Strong Morita equivalence for the Denjoy C*-Algebras

Published online by Cambridge University Press:  20 November 2018

Ian F. Putnam
Ian F. Putnam*
Affiliation:
Dalhousie UniversityHalifax, N.S. B3H 3J5, Canada
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The C*-algebras associated with irrational rotations of the circle were classified up to strong Morita equivalence by M. A. Rieffel. As a corollary, he gave a complete classification of the C*-algebras arising from irrational or Kronecker flows on the 2-torus up to *-isomorphism. Here, we extend the result to the socalled Denjoy homeomorphisms. Specifically, we give a necessary and sufficient condition for the strong Morita equivalence of two C*-algebras arising from homeomorphisms of the circle without periodic points. As a corollary, we show that two C*-algebras arising from flows on the 2-torus obtained from such homeomorphisms by the “flow under constant function” construction are *-isomorphic if and only if the flows themselves are topologically conjugate.

Keywords

47C15
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 31 , Issue 4 , 01 December 1988 , pp. 439 - 447
Copyright
Copyright © Canadian Mathematical Society 1988

References

1. Brown, L. G., Green, P., and Rieffel, M. A., Stable isomorphism and strong Morita equivalence of C*-algebras Pacific J. Math. 71 (1977), pp. 349–363.Google Scholar
2. Green, P., The structure of imprimitivity algebras J. Functional Analysis 36 (1980), pp. 88–104.Google Scholar
3. Markley, N. G., Homeomorphisms of the circle without periodic points Proc. London Math. Soc. (3) 20 (1970), pp. 688–698.Google Scholar
4. Pimsner, M. V. and Voiculescu, D., Imbedding the irrational rotation C*-algebra into an AF-algebra J. Operator Theory 4 (1980), pp. 201–210.Google Scholar
5. Pimsner, M. V., Exact sequences for K-groups and Ext-groups of certain cross-product C*-algebras J. Operator Theory 4 (1980), pp. 93–118.Google Scholar
6. Putnam, I. F., Schmidt, K. and Skau, C., C* -algebras associated with Denjoy homeomorphisms of the circle J. Operator Theory 16 (1986), pp. 99–126.Google Scholar
7. Rieffel, M. A., C*-algebras associated with irrational rotations Pacific J. Math. 93 (1981), pp. 415–429.Google Scholar
8. Rieffel, M. A., Morita equivalence for operator algebras Proc. Symp. Pure Math. 38 (1982), pp. Part 1, 285–298.Google Scholar
9. Rieffel, M. A., Applications of strong Morita equivalence to transformation group C*-algebras Proc. Symp. Pure Math. 38 (1982), Part 1, pp. 299–310.Google Scholar