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Group duality and the Kubo-Martin-Schwinger condition

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Abstract

We consider clusteringG-invariant states of aC*-algebraU endowed with an action of a locally compact abelian groupG. Denoting as usual byF AB,G AB, the corresponding two-point functions, we give criteria for the fulfillment of the KMS condition (w.r.t. some one-parameter subgroup ofG) based upon the existence of a closable mapT such thatTF AB =G AB for allA,B∈U. Closability is either inL ∞(G),B(G), orC ∞(G), according to clustering assumptions. Our criteria originate from the combination of duality results for the groupG (phrased in terms of functions systems), with density results for the two-point functions.

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Author notes

  1. M. Takesaki

    Present address: Department of Mathematics, UCLA, Hilgard Avenue, Los Angeles, California, USA

Authors and Affiliations

  1. Centre de Physique Théorique du CNRS II, Marseille-Luminy, Marseille, France

    D. Kastler & M. Takesaki

  2. Département de Physique, UER Scientifique de Marseille-Luminy, Marseille, France

    D. Kastler

  3. Département de Mathématiques, UER Scientifique de Marseille-Luminy, Marseille, France

    M. Takesaki

Authors
  1. D. Kastler
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  2. M. Takesaki
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Communicated by H. Araki

Supported in part by the National Science Foundation

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Kastler, D., Takesaki, M. Group duality and the Kubo-Martin-Schwinger condition. Commun.Math. Phys. 70, 193–212 (1979). https://doi.org/10.1007/BF01200051

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  • DOI: https://doi.org/10.1007/BF01200051

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