Noncommutative protori and inductive spectral triples
classification
🧮 math.OA
keywords
limitsnoncommutativespectraltriplesembeddingsinductiveprotoriscale
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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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