Spectral triples for nonarchimedean local fields. (English) Zbl 1429.46045

Summary: Using associated trees, we construct a spectral triple for the \(C^*\)-algebra of continuous functions on the ring of integers \(R\) of a nonarchimedean local field \(F\) of characteristic zero, and investigate its properties. Remarkably, the spectrum of the spectral triple operator is closely related to the roots of a \(q\)-hypergeometric function. We also study a noncompact version of this construction for the \(C^*\)-algebra of continuous functions on \(F\), vanishing at infinity.


46L89 Other “noncommutative” mathematics based on \(C^*\)-algebra theory
58B34 Noncommutative geometry (à la Connes)
Full Text: DOI arXiv Euclid


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