Rationally AF algebras and KMS states of Z-absorbing C*-algebras

TL;DR

This paper introduces rationally AF algebras to realize all KMS-bundles on Jiang-Su algebra, demonstrating their application in constructing flows with prescribed KMS-bundles on Z-absorbing C*-algebras.

Contribution

It defines rationally AF algebras and shows they can realize all KMS-bundles on Jiang-Su algebra within Z-absorbing C*-algebras.

Findings

Construction of flows with prescribed KMS-bundles

Existence of rationally AF algebras for given KMS-bundles

Application to irrational rotation algebra

Abstract

In order to realize all possible KMS-bundles on the Jiang-Su algebra, we introduce a class of C*-algebras which we call rationally approximately finite dimensional (RAF). Using these, we show that for a given proper simplex bundle $(S, \pi)$ with a singleton ${\pi}^{-1}(\{0\})$ and a unital separable monotracial C*-algebra $A$ absorbing the Jiang-Su algebra tensorially (for instance, the irrational rotation algebra), there exists a flow on $A$ whose KMS-bundle is isomorphic to $(S, \pi)$.