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.
Citation
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