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

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.

arXiv comment19 pages

References in corpus (8)

• KMS states of quasi-free dynamics on Pimsner algebras
• Decomposition rank of UHF-absorbing C*-algebras
• Z-stability of crossed products by strongly outer actions II
• Strict comparison and Z-absorption of nuclear C*-algebras
• Z-stability of crossed products by strongly outer actions
• Decomposition rank of approximately subhomogeneous C*-algebras
• The possible temperatures for flows on a simple AF algebra
• The bundle of KMS state spaces for flows on a unital C*-algebra