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| GENERALIZED SIMPLE NONCOMMUTATIVE TORI |
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Citation： |
C. G. PARK.GENERALIZED SIMPLE NONCOMMUTATIVE TORI[J].Chinese Annals of Mathematics B,2002,23(4):539~544 |
| Page view： 1084
Net amount： 675 |
Authors： |
C. G. PARK; |
Foundation： |
Project supported by Grant No.1999-2-102-001-3 from the Interdisciplinary Research Program Year of the KOSEF. |
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| Abstract： |
The generalized noncommutative torus $T_{\rho}^{k}$ of rank $n$ was defined in [4] by the crossed product $A_{\frac{m}{k}} \times_{\alpha_3} \Bbb Z \times_{\alpha_4}\cdots\times_{\alpha_n} \Bbb Z$, where the actions $\alpha_i$ of $\Bbb Z$ on the fibre $M_k(\Bbb C)$ of a rational rotation algebra $A_{\frac{m}{k}}$ are trivial, and $C^*(k\Bbb Z \times k\Bbb Z) \times_{\alpha_3} \Bbb Z \times_{\alpha_4} \cdots \times_{\alpha_n} \Bbb Z$ is a completely irrational noncommutative torus $A_{\rho}$ of rank $n$. It is shown in this paper that $T^k_{\rho}$ is strongly Morita equivalent to $A_{\rho}$, and that $T_{\rho}^{k} \otimes M_{p^{\infty}}$ is isomorphic to $A_{\rho} \otimes M_{k}(\Bbb C) \otimes M_{p^{\infty}}$ if and only if the set of prime factors of $k$ is a subset of the set of prime factors of $p$. |
Keywords： |
Noncommutative torus, Equivalence bimodule, UHF-algebra, Cuntz algebra, Crossed product |
Classification： |
46L05, 46L87 |
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