A $P$-Adic Spectral Triple
Operator Algebras
2015-06-19 v2
Abstract
We construct a spectral triple for the C-algebra of continuous functions on the space of -adic integers by using a rooted tree obtained from coarse-grained approximation of the space, and the forward derivative on the tree. Additionally, we verify that our spectral triple satisfies the properties of a compact spectral metric space, and we show that the metric on the space of -adic integers induced by the spectral triple is equivalent to the usual -adic metric.
Cite
@article{arxiv.1403.7263,
title = {A $P$-Adic Spectral Triple},
author = {Slawomir Klimek and Matt McBride and Sumedha Rathnayake},
journal= {arXiv preprint arXiv:1403.7263},
year = {2015}
}