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The Factor Type of Conservative KMS-Weights on Graph \(C^*\)-Algebras

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Analysis and Operator Theory

Part of the book series: Springer Optimization and Its Applications ((SOIA,volume 146))

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Abstract

We determine the factor generated by the GNS-representation defined by a KMS-weight for a generalized gauge action on a simple graph \(C^*\)-algebra, when the corresponding measure on the path space of the graph is conservative for the shift.

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Notes

  1. 1.

    Despite some effort to make this a complete list, presumably it is not.

  2. 2.

    Note that we apply the definition from [23] for the action \(\alpha _{-t}\) in order to use the same sign convention as in [1], for example.

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Acknowledgements

I am grateful to Johannes Christensen for discussions and help to eliminate mistakes. The work was supported by the DFF-Research Project 2 ‘Automorphisms and Invariants of Operator Algebras’, no. 7014-00145B.

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Authors and Affiliations

  1. Department of Mathematics, University of Aarhus, Aarhus, Denmark

    Klaus Thomsen

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  1. Klaus Thomsen
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Correspondence to Klaus Thomsen .

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Editors and Affiliations

  1. National Technical University of Athens, Athens, Greece

    Themistocles M. Rassias

  2. Institute of Mathematics, Aix-Marseille University, Marseille, France

    Valentin A. Zagrebnov

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Thomsen, K. (2019). The Factor Type of Conservative KMS-Weights on Graph \(C^*\)-Algebras. In: Rassias, T.M., Zagrebnov, V.A. (eds) Analysis and Operator Theory . Springer Optimization and Its Applications, vol 146. Springer, Cham. https://doi.org/10.1007/978-3-030-12661-2_17

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