On the bundle of KMS state spaces for flows on a Z-absorbing C*-algebra
Operator Algebras
2022-06-15 v1
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.
Cite
@article{arxiv.2112.13336,
title = {On the bundle of KMS state spaces for flows on a Z-absorbing C*-algebra},
author = {George A. Elliott and Yasuhiko Sato and Klaus Thomsen},
journal= {arXiv preprint arXiv:2112.13336},
year = {2022}
}
Comments
19 pages