The admissible KMS bundles on classifiable C$^*$-algebras

Abstract

Given any unital, finite, classifiable C$^*$-algebra $A$ with real rank zero and any compact simplex bundle with the fibre at zero being homeomorphic to the space of tracial states on $A$, we show that there exists a flow on $A$ realising this simplex. Moreover, we show that given any unital UCT Kirchberg algebra $A$ and any proper simplex bundle with empty fibre at zero, there exists a flow on $A$ realising this simplex.