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

Klimek, Slawomir; Rathnayake, Sumedha; Sakai, Kaoru

Rocky Mt. J. Math. 49, No. 4, 1259-1291 (2019).

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.

MSC:

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

Keywords:

spectral triple; nonarchimedean local fields

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