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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
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Abstract

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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

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