Equivalence Bimodule between Spherical Noncommutative Tori

Abstract

Let ni,mj > 1. In [5], the sperical noncommutative torus \(S_p^{pd} \) was defined by twisting \(\widehat{T^{r + 2} } \times Z^l \) in \(T^{pd} \otimes C*\left( {Z^l } \right)\) by a totally skew multiplier p on \(\widehat{T^{r + 2} \times Z^l }\) for Tpd a pd-homogeneous C*-algebra over \(\prod\nolimits_{i = 1}^{s_4 } {S^{2n_i } } \times \prod\nolimits^{s_2 } {S^2 } \times \prod\nolimits_{j = 1}^{s_3 } {S^{2m_j - 1} } \times \prod\nolimits^{s_1 } {S^1 } \times T^{r + 2}\). It is shown that \(S_p^{pd}\) is strongly Morita equivalent to \(C\left( {\prod\nolimits_{i = 1}^{s_4 } {S^{2n_i } } \times \prod\nolimits^{s_2 } {S^2 } \times \prod\nolimits_{J = 1}^{s_3 } {S^{2m_j - 1} } \times \prod\nolimits^{s^1 } {S^1 } } \right) \otimes C*\left( {\widehat{T^{r + 2} } \times Z^l ,p} \right)\).