Spatial realisations of KMS states on the C*-algebras of higher-rank graphs

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:427

Article

Huef, Astrid An¹  Kang, Sooran¹  Raeburn, Iain¹ 

[1] Univ Otago, Dept Math & Stat, Dunedin 9054, New Zealand

关键词: Toeplitz algebra;    Higher-rank graph;    Gauge action;    KMS state;   

DOI  :  10.1016/j.jmaa.2015.02.045

来源: Elsevier

【 摘 要 】

Several authors have recently been studying the equilibrium or KMS states on the Toeplitz algebras of finite higher-rank graphs. For graphs of rank one (that is, for ordinary directed graphs), there is a natural dynamics obtained by lifting the gauge action of the circle to an action of the real line. The algebras of higher-rank graphs carry a gauge action of a higher-dimensional torus, and there are many potential dynamics arising from different embeddings of the real line in the torus. Previous results show that there is nonetheless a preferred dynamics for which the system exhibits a particularly satisfactory phase transition, and that the unique KMS state at the critical inverse temperature can then be implemented by integrating vector states against a measure on the infinite path space of the graph. Here we obtain a similar description of the KMS state at the critical inverse temperature for other dynamics. Our spatial implementation is given by integrating against a measure on a space of paths which are infinite in some directions but finite in others. Our results are sharpest for the algebras of rank-two graphs. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free