Chun-Gil Park

Abstract
Let $A_{cd}$ be a $cd$-homogeneous $C^*$-algebra over $\prod^eS^{2}\times \prod^{s}S^{1} \times \Bbb T^{r+2}$ of which no non-trivial matrix algebra can be factored out. The spherical non-commutative torus $\Bbb S_{\rho}^{cd}$ is defined by twisting $C^*(\widehat{\Bbb T^{r+2}} \times \Bbb Z^{m-2})$  in $A_{cd} \otimes C^*(\Bbb Z^{m-2})$  by a totally skew multiplier $\rho$ on $\widehat{\Bbb T^{r+2}}  \times \Bbb Z^{m-2}$. It is shown that $\Bbb S_{\rho}^{cd} \otimes M_{p^{\infty}}$ is isomorphic to $C(\prod^eS^{2}\times \prod^{s}S^{1}) \otimes C^*(\widehat{\Bbb T^{r+2}}  \times \Bbb Z^{m-2}, \rho) \otimes M_{cd}(\Bbb C) \otimes M_{p^{\infty}}$ if and only if the set of prime factors of $cd$ is a subset of the set of prime factors of $p$.