TY - JOUR

T1 - On the Bundle of KMS State Spaces for Flows on a Z -Absorbing C*-Algebra

AU - Elliott, George A.

AU - Sato, Yasuhiko

AU - Thomsen, Klaus

N1 - Publisher Copyright:
© 2022, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.

PY - 2022/7

Y1 - 2022/7

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85131097848&partnerID=8YFLogxK

U2 - 10.1007/s00220-022-04386-x

DO - 10.1007/s00220-022-04386-x

M3 - Journal article

AN - SCOPUS:85131097848

SN - 0010-3616

VL - 393

SP - 1105

EP - 1123

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

IS - 2

ER -