Abstract
The non-commutative torus C *(ℝn,ω) is realized as the C*-algebra of sections of a locally trivial C*-algebra bundle over Sω with fibres isomorphic to C *ℝn/Sω, ω1) for a totally skew multiplier ω1 on ℝn/Sω. D. Poguntke [9] proved that A ω is stably isomorphic to C(Sω) ⊗ C(*(∝ Zn/Sω, ω1) ≅ C(Sω) ⊗ Aφ ⊗ Mkl(∝ 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(Sω) ⊗ Aφ-equivalence bimodule.
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