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

George A. Elliott; Yasuhiko Sato; Klaus Thomsen

doi:10.1007/s00220-022-04386-x

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

George A. Elliott^*, Yasuhiko Sato, Klaus Thomsen

^*Corresponding author af dette arbejde

Institut for Matematik

Publikation: Bidrag til tidsskrift/Konferencebidrag i tidsskrift /Bidrag til avis › Tidsskriftartikel › Forskning › peer review

Abstract

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.

Originalsprog	Engelsk
Tidsskrift	Communications in Mathematical Physics
Vol/bind	393
Nummer	2
Sider (fra-til)	1105-1123
Antal sider	19
ISSN	0010-3616
DOI	https://doi.org/10.1007/s00220-022-04386-x
Status	Udgivet - jul. 2022

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10.1007/s00220-022-04386-x

https://arxiv.org/pdf/2112.13336.pdf

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

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