Geodesic
Explicit equivalence bimodules for rotation algebras
Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial and algoritmic methods. Part X, Tome 307 (2004), pp. 175-188 Cet article a éte moissonné depuis la source Math-Net.Ru

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$C^*$-algebras associated with irrational rotations are Morita equivalent iff the rotation parameters belong to the same orbit under the action of $GL(2,Z)$. In this note we offer explicit type II representations such that the bimodule is dense in the corresponding Hilbert space. 
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     title = {Explicit equivalence bimodules for rotation algebras},
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H. Narnhofer. Explicit equivalence bimodules for rotation algebras. Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial and algoritmic methods. Part X, Tome 307 (2004), pp. 175-188. http://geodesic.mathdoc.fr/item/ZNSL_2004_307_a5/

[1] M. A. Rieffel, “$C^*$-algebras associated with irrational rotations”, Pacific J. Math., 93:2 (1981), 415–429 | MR | Zbl

[2] L. D. Faddeev, “Discrete Heisenberg–Weyl group and modular group”, Lett. Math. Phys., 34 (1995), 249–254 | DOI | MR | Zbl

[3] A. M. Vershik, Strange factor representations of type $II_1$, and pairs of dual dynamical systems, arXiv: /math.OA/0302141 | MR

[4] A. Connes, Noncommutative geometry, Academic Press, San Diego, 1994 | MR | Zbl