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

Astrid an Huef; Marcelo Laca; Iain Raeburn; Aidan Sims

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arXiv · 1404.6819

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

Astrid an Huef·Marcelo Laca·Iain Raeburn·Aidan Sims

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Abstract

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.

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BibTeX RIS

Astrid an Huef, Marcelo Laca, Iain Raeburn, Aidan Sims. 2014-04-27. KMS states on the C*-algebra of a higher-rank graph and periodicity in the path space. https://arxiv.org/abs/1404.6819

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