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KMS states on the C*-algebra of a higher-rank graph and periodicity in the path space

Journal Article


Abstract


  • © 2014 Elsevier Inc. We study the KMS states of the C*-algebra of a strongly connected finite k-graph. We find that there is only one 1-parameter subgroup of the gauge action that can admit a KMS state. The extreme KMS states for this preferred dynamics are parameterised by the characters of an abelian group that captures the periodicity in the infinite-path space of the graph. We deduce that there is a unique KMS state if and only if the k-graph C*-algebra is simple, giving a complete answer to a question of Yang. When the k-graph C*-algebra is not simple, our results reveal a phase change of an unexpected nature in its Toeplitz extension.

Publication Date


  • 2015

Citation


  • An Huef, A., Laca, M., Raeburn, I. F. & Sims, A. D. (2015). KMS states on the C*-algebra of a higher-rank graph and periodicity in the path space. Journal of Functional Analysis, 268 (7), 1840-1875.

Scopus Eid


  • 2-s2.0-84923521186

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/3755

Has Global Citation Frequency


Number Of Pages


  • 35

Start Page


  • 1840

End Page


  • 1875

Volume


  • 268

Issue


  • 7

Place Of Publication


  • United States

Abstract


  • © 2014 Elsevier Inc. We study the KMS states of the C*-algebra of a strongly connected finite k-graph. We find that there is only one 1-parameter subgroup of the gauge action that can admit a KMS state. The extreme KMS states for this preferred dynamics are parameterised by the characters of an abelian group that captures the periodicity in the infinite-path space of the graph. We deduce that there is a unique KMS state if and only if the k-graph C*-algebra is simple, giving a complete answer to a question of Yang. When the k-graph C*-algebra is not simple, our results reveal a phase change of an unexpected nature in its Toeplitz extension.

Publication Date


  • 2015

Citation


  • An Huef, A., Laca, M., Raeburn, I. F. & Sims, A. D. (2015). KMS states on the C*-algebra of a higher-rank graph and periodicity in the path space. Journal of Functional Analysis, 268 (7), 1840-1875.

Scopus Eid


  • 2-s2.0-84923521186

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/3755

Has Global Citation Frequency


Number Of Pages


  • 35

Start Page


  • 1840

End Page


  • 1875

Volume


  • 268

Issue


  • 7

Place Of Publication


  • United States