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Constructing KMS states from infinite-dimensional spectral triples

Journal Article


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.

Authors


  •   GOFFENG, MAGNUS (external author)
  •   Rennie, Adam C.
  •   Usachev, Alexandr (external author)

Publication Date


  • 2019

Citation


  • Goffeng, M., Rennie, A. & Usachev, A. (2019). Constructing KMS states from infinite-dimensional spectral triples. Journal of Geometry and Physics, 143 107-149.

Scopus Eid


  • 2-s2.0-85066249578

Number Of Pages


  • 42

Start Page


  • 107

End Page


  • 149

Volume


  • 143

Place Of Publication


  • Netherlands

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.

Authors


  •   GOFFENG, MAGNUS (external author)
  •   Rennie, Adam C.
  •   Usachev, Alexandr (external author)

Publication Date


  • 2019

Citation


  • Goffeng, M., Rennie, A. & Usachev, A. (2019). Constructing KMS states from infinite-dimensional spectral triples. Journal of Geometry and Physics, 143 107-149.

Scopus Eid


  • 2-s2.0-85066249578

Number Of Pages


  • 42

Start Page


  • 107

End Page


  • 149

Volume


  • 143

Place Of Publication


  • Netherlands