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

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On the Bundle of KMS State Spaces for Flows on a Z -Absorbing C*-Algebra. / Elliott, George A.; Sato, Yasuhiko; Thomsen, Klaus.
In: Communications in Mathematical Physics, Vol. 393, No. 2, 07.2022, p. 1105-1123.

Research output: Contribution to journal/Conference contribution in journal/Contribution to newspaper › Journal article › Research › peer-review

Harvard

Elliott, GA, Sato, Y & Thomsen, K 2022, 'On the Bundle of KMS State Spaces for Flows on a Z -Absorbing C*-Algebra', Communications in Mathematical Physics, vol. 393, no. 2, pp. 1105-1123. https://doi.org/10.1007/s00220-022-04386-x

APA

Elliott, G. A., Sato, Y., & Thomsen, K. (2022). On the Bundle of KMS State Spaces for Flows on a Z -Absorbing C*-Algebra. Communications in Mathematical Physics, 393(2), 1105-1123. https://doi.org/10.1007/s00220-022-04386-x

CBE

Elliott GA, Sato Y, Thomsen K. 2022. On the Bundle of KMS State Spaces for Flows on a Z -Absorbing C*-Algebra. Communications in Mathematical Physics. 393(2):1105-1123. https://doi.org/10.1007/s00220-022-04386-x

MLA

Elliott, George A., Yasuhiko Sato, and Klaus Thomsen. "On the Bundle of KMS State Spaces for Flows on a Z -Absorbing C*-Algebra". Communications in Mathematical Physics. 2022, 393(2). 1105-1123. https://doi.org/10.1007/s00220-022-04386-x

Vancouver

Elliott GA, Sato Y, Thomsen K. On the Bundle of KMS State Spaces for Flows on a Z -Absorbing C*-Algebra. Communications in Mathematical Physics. 2022 Jul;393(2):1105-1123. doi: 10.1007/s00220-022-04386-x

Author

Elliott, George A. ; Sato, Yasuhiko ; Thomsen, Klaus. / On the Bundle of KMS State Spaces for Flows on a Z -Absorbing C*-Algebra. In: Communications in Mathematical Physics. 2022 ; Vol. 393, No. 2. pp. 1105-1123.

Bibtex

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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.",
author = "Elliott, {George A.} and Yasuhiko Sato and Klaus Thomsen",
note = "Publisher Copyright: {\textcopyright} 2022, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.",
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RIS

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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.

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