Bulletin of the
Korean Mathematical Society BKMS

We give an easy proof of the fact that every noncommutative torus $A_{\omega}$ is stably isomorphic to the noncommutative torus $C(\widehat{S_{\omega}}) \otimes A_{\rho}$ which has a trivial bundle structure. It is well known that stable isomorphism of two separable $C^*$-algebras is equivalent to the existence of equivalence bimodule between them, and we construct a concrete equivalence bimodule between the two stably isomorphic $C^*$-algebras $A_{\omega}$ and $C(\widehat{S_{\omega}}) \otimes A_{\rho}$.

Keywords: twisted group $C^*$-algebra, crossed product, tensor product, $C^*$-algebra bundle, equivalence bimodule

MSC numbers: Primary 46L65, 46L87