| Title:
|
Equivalence bimodule between non-commutative tori (English) |
| Author:
|
Oh, Sei-Qwon |
| Author:
|
Park, Chun-Gil |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
53 |
| Issue:
|
2 |
| Year:
|
2003 |
| Pages:
|
289-294 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The non-commutative torus $C^*(\mathbb{Z}^n,\omega )$ is realized as the $C^*$-algebra of sections of a locally trivial $C^*$-algebra bundle over $\widehat{S_{\omega }}$ with fibres isomorphic to $C^*(\mathbb{Z}^n/S_{\omega }, \omega _1)$ for a totally skew multiplier $\omega _1$ on $\mathbb{Z}^n/S_{\omega }$. D. Poguntke [9] proved that $A_{\omega }$ is stably isomorphic to $C(\widehat{S_{\omega }}) \otimes C^*(\mathbb{Z}^n/S_{\omega }, \omega _1) \cong C(\widehat{S_{\omega }}) \otimes A_{\varphi } \otimes M_{kl}(\mathbb{C})$ for a simple non-commutative torus $A_{\varphi }$ 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 $A_{\omega }$-$C(\widehat{S_{\omega }}) \otimes A_{\varphi }$-equivalence bimodule. (English) |
| Keyword:
|
Morita equivalent |
| Keyword:
|
twisted group $C^*$-algebra |
| Keyword:
|
crossed product |
| MSC:
|
46L05 |
| MSC:
|
46L87 |
| MSC:
|
46L89 |
| MSC:
|
55R15 |
| idZBL:
|
Zbl 1028.46102 |
| idMR:
|
MR1983452 |
| . |
| Date available:
|
2009-09-24T11:01:35Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127800 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
|
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| Reference:
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| Reference:
|
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| Reference:
|
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| Reference:
|
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