Rationally AF Algebras and KMS States of $\mathcal{Z}$-Absorbing ${\mathrm{C}}^{\ast }$-Algebras

Abstract

In order to realize all possible KMS-bundles on the Jiang–Su algebra, we introduce a class of ${\mathrm{C}}^{\ast }$-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 ${\mathrm{C}}^{\ast }$-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 $(S,\pi )$.