A $P$-Adic Spectral Triple

Abstract

We construct a spectral triple for the C${}^{\ast }$-algebra of continuous functions on the space of $p$-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 $p$-adic integers induced by the spectral triple is equivalent to the usual $p$-adic metric.

References in corpus (3)

• Spectral triples for AF C*-algebras and metrics on the Cantor set
• Dynamical Systems on Spectral Metric Spaces
• On the spectral characterization of manifolds

Cited by in corpus (1)

• Spectral Triples for nonarchimedean local fields