Spectral Triples for nonarchimedean local fields

Abstract

Using associated trees, we construct a spectral triple for the C${}^{\ast }$-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 non compact version of this construction for the C${}^{\ast }$-algebra of continuous functions on $F$, vanishing at infinity.

References in corpus (3)

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