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arXiv · 2605.26049

Noncommutative protori and inductive spectral triples

Remus Floricel·Patrick Melanson
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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.

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Remus Floricel, Patrick Melanson. 2026-05-25. Noncommutative protori and inductive spectral triples. https://arxiv.org/abs/2605.26049

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