Equivalence Bimodule Between Non-Commutative Tori

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The non-commutative torus C*(ℤn,ω) is realized as the C*-algebra of sections of a locally trivial C*-algebra bundle over Symbol with fibres isomorphic to C*(ℤn/Sω1) for a totally skew multiplier ω1 on ℤn/Sω. D. Poguntke [9] proved that Aω is stably isomorphic to C(Symbol) ⊗ C*(ℤn/Sω, ω1) ≅ C(Symbol) ⊗ AϕMkl(ℂ) for a simple non-commutative torus Aϕ and an integer kl. It is well-known that a stable isomorphism of two separable C*-algebras is equivalent to the existence of equivalence bimodule between them. We construct an Aω-C(Symbol) ⊗ Aϕ-equivalence bimodule.

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