Noncommutative protori and inductive spectral triples
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866917532250669056 |
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| author | Floricel, Remus Melanson, Patrick |
| author_facet | Floricel, Remus Melanson, Patrick |
| contents | We study inductive limits of higher-dimensional noncommutative tori, which we call noncommutative protori. We compute the Elliott invariants for broad classes of unital and nonunital systems, including toric maps, Morita-corner embeddings, and dimension-changing and proper embeddings. For the resulting simple limits we determine explicitly the ordered $K$-groups, trace cone, scale, and projection scale, yielding concrete classification criteria. We also construct compatible spectral triples and locally compact spectral triples on these limits via Fourier- and Morita-compatible Dirac structures. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_26049 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Noncommutative protori and inductive spectral triples Floricel, Remus Melanson, Patrick Operator Algebras 46L05, 46L35, 58B34 We study inductive limits of higher-dimensional noncommutative tori, which we call noncommutative protori. We compute the Elliott invariants for broad classes of unital and nonunital systems, including toric maps, Morita-corner embeddings, and dimension-changing and proper embeddings. For the resulting simple limits we determine explicitly the ordered $K$-groups, trace cone, scale, and projection scale, yielding concrete classification criteria. We also construct compatible spectral triples and locally compact spectral triples on these limits via Fourier- and Morita-compatible Dirac structures. |
| title | Noncommutative protori and inductive spectral triples |
| topic | Operator Algebras 46L05, 46L35, 58B34 |
| url | https://arxiv.org/abs/2605.26049 |