On the extension of higher-dimensional noncommutative tori (Q2754837)
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scientific article; zbMATH DE number 1668457
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the extension of higher-dimensional noncommutative tori |
scientific article; zbMATH DE number 1668457 |
Statements
4 November 2001
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noncommutative torus
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Fock representation
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0.9254418
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0.92384756
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0.91816777
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0.9161004
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On the extension of higher-dimensional noncommutative tori (English)
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The author studies the \(C^*\)-algebra generated by isometries satisfying the relations NEWLINE\[NEWLINE s_is_j^*=e^{2\pi i\theta_{ij}}s_js_i^*,\quad s_js_i=e^{2\pi i\theta_{ij}}s_is_j,\quad j=1,\ldots ,d. NEWLINE\]NEWLINE It is proved that in the case of rational parameters \(\theta_{ij}\) the Fock representation is faithful. In the case of two generators the structure of the ideal generated by the projections \(1-s_is_i^*\) is described.
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