On the Bundle of KMS State Spaces for Flows on a Z -Absorbing C*-Algebra

George A. Elliott, Yasuhiko Sato, Klaus Thomsen

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A complete characterization is given of the collection of KMS state spaces for a flow on the Jiang-Su C*-algebra in the case that the set of inverse temperatures is bounded. Namely, it is an arbitrary compact simplex bundle over the (compact) set of inverse temperatures with fibre at zero a single point. (Hence this holds for the tensor product of this C*-algebra with any unital C*-algebra with unique trace state.) An analogous characterization is given for arbitrary flows on a (Kirchberg–Phillips) classifiable infinite unital simple C*-algebra: for each such algebra the KMS states form an arbitrary proper simplex bundle (the inverse image of a compact set of inverse temperatures is compact) such that the fibre at zero is empty.

Original languageEnglish
Pages (from-to)1105-1123
Number of pages19
JournalCommunications in Mathematical Physics
Issue number2
Publication statusPublished - Jul 2022

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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