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Constructing KMS states from infinite-dimensional spectral triples

Journal article
Authors Magnus Goffeng
A. Rennie
Alexandr Usachev
Published in Journal of Geometry and Physics
Volume 143
Pages 107-149
ISSN 0393-0440
Publication year 2019
Published at Department of Mathematical Sciences
Pages 107-149
Language en
Links dx.doi.org/10.1016/j.geomphys.2019....
Keywords Kasparov module, KMS-state, spectral triple, Summability
Subject categories Mathematics

Abstract

We construct KMS-states from Li1-summable semifinite spectral triples and show that in several important examples the construction coincides with well-known direct constructions of KMS-states for naturally defined flows. Under further summability assumptions the constructed KMS-state can be computed in terms of Dixmier traces. For closed manifolds, we recover the ordinary Lebesgue integral. For Cuntz–Pimsner algebras with their gauge flow, the construction produces KMS-states from traces on the coefficient algebra and recovers the Laca–Neshveyev correspondence. For a discrete group acting on its Stone–Čech boundary, we recover the Patterson–Sullivan measures on the Stone-Čech boundary for a flow defined from the Radon–Nikodym cocycle. © 2019 Elsevier B.V.

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