Geodesic
Strong Morita equivalence for the Denjoy C*-Algebras
Canadian mathematical bulletin, Tome 31 (1988) no. 4, pp. 439-447

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DOI

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.
DOI : 10.4153/CMB-1988-064-7
Mots-clés : 47C15 
Putnam, Ian F. Strong Morita equivalence for the Denjoy C*-Algebras. Canadian mathematical bulletin, Tome 31 (1988) no. 4, pp. 439-447. doi: 10.4153/CMB-1988-064-7
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     author = {Putnam, Ian F.},
     title = {Strong {Morita} equivalence for the {Denjoy} {C*-Algebras}},
     journal = {Canadian mathematical bulletin},
     pages = {439--447},
     year = {1988},
     volume = {31},
     number = {4},
     doi = {10.4153/CMB-1988-064-7},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1988-064-7/}
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