Spectral Triples on noncommutative solenoids from the standard spectral triples on quantum tori
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866908886422781952 |
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| author | Farsi, Carla Latremoliere, Frederic Packer, Judith |
| author_facet | Farsi, Carla Latremoliere, Frederic Packer, Judith |
| contents | We address the natural question: as noncommutative solenoids are inductive limits of quantum tori, do the standard spectral triples on quantum tori converge to some spectral triple on noncommutative solenoid for the spectral propinquity? We answer this question by showing that, using appropriate bounded perturbation of the spectral triples on quantum tori, such a spectral triple on noncommutative solenoid can be constructed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_16323 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Spectral Triples on noncommutative solenoids from the standard spectral triples on quantum tori Farsi, Carla Latremoliere, Frederic Packer, Judith Operator Algebras 46L89 We address the natural question: as noncommutative solenoids are inductive limits of quantum tori, do the standard spectral triples on quantum tori converge to some spectral triple on noncommutative solenoid for the spectral propinquity? We answer this question by showing that, using appropriate bounded perturbation of the spectral triples on quantum tori, such a spectral triple on noncommutative solenoid can be constructed. |
| title | Spectral Triples on noncommutative solenoids from the standard spectral triples on quantum tori |
| topic | Operator Algebras 46L89 |
| url | https://arxiv.org/abs/2403.16323 |