Constructing KMS states from infinite-dimensional spectral triples
Abstract
We construct KMS-states from -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-\v{C}ech boundary, we recover the Patterson-Sullivan measures on the Stone-\v{C}ech boundary for a flow defined from the Radon-Nikodym cocycle.
Cite
@article{arxiv.1811.06923,
title = {Constructing KMS states from infinite-dimensional spectral triples},
author = {Magnus Goffeng and Adam Rennie and Alexandr Usachev},
journal= {arXiv preprint arXiv:1811.06923},
year = {2019}
}
Comments
66 pages