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2019 Spectral triples for nonarchimedean local fields
Slawomir Klimek, Sumedha Rathnayake, Kaoru Sakai
Rocky Mountain J. Math. 49(4): 1259-1291 (2019). DOI: 10.1216/RMJ-2019-49-4-1259

Abstract

Using associated trees, we construct a spectral triple for the $\mathrm {C}^*$-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 $\mathrm {C}^*$-algebra of continuous functions on $F$, vanishing at infinity.

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Slawomir Klimek. Sumedha Rathnayake. Kaoru Sakai. "Spectral triples for nonarchimedean local fields." Rocky Mountain J. Math. 49 (4) 1259 - 1291, 2019. https://doi.org/10.1216/RMJ-2019-49-4-1259

Information

Published: 2019
First available in Project Euclid: 29 August 2019

zbMATH: 07104717
MathSciNet: MR3998921
Digital Object Identifier: 10.1216/RMJ-2019-49-4-1259

Subjects:
Primary: 58B34
Secondary: 46L89

Rights: Copyright © 2019 Rocky Mountain Mathematics Consortium

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Vol.49 • No. 4 • 2019
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