On the bundle of KMS state spaces for flows on a Z-absorbing C*-algebra

TL;DR

This paper characterizes the structure of KMS state spaces for flows on Z-absorbing C*-algebras, showing how they can be realized as KMS bundles in various algebraic settings, revealing rich diversity in flow classifications.

Contribution

It constructs specific flows with prescribed KMS bundles on Jiang-Su and purely infinite nuclear C*-algebras, advancing understanding of their state space structures.

Findings

Every compact simplex bundle with one point over 0 is a KMS bundle on Jiang-Su algebra.

Uncountably many non-approximately inner flows exist on certain Z-absorbing algebras.

Proper simplex bundles with empty fiber over 0 are realizable as KMS bundles on purely infinite nuclear C*-algebras.

Abstract

We obtain three results: 1) Every compact simplex bundle with exactly one point in the fiber over 0 is the KMS bundle of a periodic flow on the Jiang-Su algebra. 2) Let A be a separable unital C*-algebra with a unique trace state. Suppose that A tensorially absorbs the Jiang-Su algebra. The (weak) cocycle-conjugacy classes of flows that are not approximately inner are uncountable. 3) Let B be a separable, simple, unital, purely infinite and nuclear C*-algebra in the UCT class. Assume that the K1 group of B is torsion free. Every proper simplex bundle with empty fiber over 0 is the KMS bundle of a periodic flow on B.