The Bundle of KMS State Spaces for Flows on a Unital AF C*-algebra

C. R. Math. Rep. Acad. Sci. Canada Vol. 43 (4) 2021, pp. 103-121
(Received: 2021-09-21 )

George A. Elliott, Department of Mathematics, University of Toronto, Toronto, Ontario, Canada M5S 2E4; e-mail:

Klaus Thomsen, Department of Mathematics, Aarhus University, Ny Munkegade, 8000 Aarhus C, Denmark; e-mail:


It is shown that, for any unital simple infinite-dimensional AF algebra, the KMS-state bundle for a one-parameter automorphism group is isomorphic to an arbitrary proper simplex bundle over the real line with (as is necessary) fibre at (inverse temperature) zero isomorphic to the trace simplex.

On démontre que, pour toute C*-algèbre AF simple à élément unité et à dimension infinie, le faisceau d’états KMS pour un grouped’automorphismes à un paramètre est isomorphe à un faisceau de simplices propre arbitraire sur la ligne réelle tel que (nécessairement) le fibre sur la température inverse zéro est isomorphe au simplex tracial.

Keywords: One-parameter automorphism group of an AF algebra, bundle of equilibrium (KMS) states arbitrary

AMS Subject Classification: General theory of $C^*$-algebras, Noncommutative dynamical systems 46L05, 46L55

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