Noncommutative protori and inductive spectral triples
Operator Algebras
2026-05-26 v1
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 -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.
Cite
@article{arxiv.2605.26049,
title = {Noncommutative protori and inductive spectral triples},
author = {Remus Floricel and Patrick Melanson},
journal= {arXiv preprint arXiv:2605.26049},
year = {2026}
}