Constructing KMS states from infinite-dimensional spectral triples

Abstract

We construct KMS-states from ${\mathrm{Li}}_1$-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.

66 pages

References in corpus (9)

• Amenable actions and exactness for discrete groups
• KMS states of quasi-free dynamics on Pimsner algebras
• Index theory for locally compact noncommutative geometries
• Twisted cyclic theory, equivariant KK theory and KMS States
• Shift tail equivalence and an unbounded representative of the Cuntz-Pimsner extension
• Spectral flow invariants and twisted cyclic theory from the Haar state on SU_q(2)
• C^*-algebras associated with self-similar sets
• Wieler solenoids, Cuntz-Pimsner algebras and K-theory
• Poincare duality for Cuntz-Pimsner algebras of bimodules

Cited by in corpus (4)

• Untwisting twisted spectral triples
• A noncommutative integral on spectrally truncated spectral triples, and a link with quantum ergodicity
• The odd spectral localiser via asymptotic morphisms and quasi-projections
• Asymptotic Behaviour of Semigroup Traces and Schatten Classes of Resolvents