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

Authors

Astrid An Huef, University of WollongongFollow
Marcelo Laca, University of WollongongFollow
Iain F. Raeburn, University of OtagoFollow
Aidan Sims, University of WollongongFollow

RIS ID

97805

Publication Details

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.

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.