Abstract: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.
| Subjects: | Operator Algebras (math.OA) |
| MSC classes: | 46L05, 46L35, 58B34 |
| Cite as: | arXiv:2605.26049 [math.OA] |
| (or arXiv:2605.26049v1 [math.OA] for this version) | |
| https://doi.org/10.48550/arXiv.2605.26049 arXiv-issued DOI via DataCite (pending registration) |
From: Remus Floricel [view email]
[v1]
Mon, 25 May 2026 17:11:38 UTC (73 KB)
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