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The Possible Temperatures for Flows on a Simple AF Algebra

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Abstract

It is shown that for any unital infinite dimensional simple AF algebra A and for any lower bounded closed set K of real numbers containing zero there is a flow on A such that the set inverse temperatures is exactly K.

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Notes

  1. It has been pointed out to me that stability of \(B \rtimes _{\gamma } {\mathbb {Z}}\) also follows from [HR].

  2. Theorem 3.10 in [E2] is very general and the argument concerning Riesz groups uses the decomposition property. However, a major step in the proof of Lemma 3.2 in [BEK] gives the arguments directly for the interpolation property, albeit in the colexicographic order.

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Acknowledgements

I am grateful to Y. Sato for comments on the first version of this paper which helped me navigate in the litterature on the classification of simple \(C^*\)-algebras, and I thank the referee of [Th5] for his remarks. The work was supported by the DFF-Research Project 2 ‘Automorphisms and Invariants of Operator Algebras’, No. 7014-00145B.

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  1. Department of Mathematics, Aarhus University, Ny Munkegade, 8000, Aarhus C, Denmark

    Klaus Thomsen

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Communicated by H.-T. Yau

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Thomsen, K. The Possible Temperatures for Flows on a Simple AF Algebra. Commun. Math. Phys. 386, 1489–1518 (2021). https://doi.org/10.1007/s00220-021-04130-x

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