Constructing KMS states from infinite-dimensional spectral triples
Journal article, 2019

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.

KMS-state

Kasparov module

spectral triple

Summability

Author

Magnus C H T Goffeng

Chalmers, Mathematical Sciences, Analysis and Probability Theory

Adam Rennie

University of Wollongong

Alexandr Usachev

Chalmers, Mathematical Sciences, Analysis and Probability Theory

Journal of Geometry and Physics

0393-0440 (ISSN)

Vol. 143 107-149

Subject Categories

Algebra and Logic

Computational Mathematics

Geometry

DOI

10.1016/j.geomphys.2019.05.006

More information

Latest update

7/12/2019