SPECTRAL TRIPLES FOR NONARCHIMEDEAN LOCAL FIELDS

摘要

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.