KMS states on C*-algebras associated to a family of *-commuting local homeomorphisms

被引：7
作者：
Afsar, Zahra [1 ]
Huef, Astrid An [2 ,3 ]
Raeburn, Iain [2 ,3 ]
机构：
[1] Univ Wollongong, Sch Math & Appl Stat, Wollongong, NSW 2522, Australia
[2] Univ Otago, Dept Math & Stat, POB 56, Dunedin 9054, New Zealand
[3] Victoria Univ Wellington, Sch Math & Stat, POB 56, Wellington 6140, New Zealand
来源：
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2018年 / 464卷 / 02期
关键词：
Product system; (*)-Commuting homeomorphisms; Toeplitz algebra; Nica-Toeplitz algebra; Cuntz-Pimsner algebra; KMS state; PRODUCT SYSTEMS; DYNAMICAL-SYSTEMS; PIMSNER ALGEBRAS; SEMIGROUPS; GRAPH;
D O I：
10.1016/j.jmaa.2018.01.013
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We consider a family of *-commuting local homeomorphisms on a compact space, and build a compactly aligned product system of Hilbert bimodules. The Nica-Toeplitz algebra of this system carries a gauge action of a higher-dimensional torus, and there are many possible dynamics obtained by composing with different embeddings of the real line in this torus. We study the KMS states of these dynamics. For large inverse temperatures including infinity, we describe the simplex of KMS states on the Nica-Toeplitz algebra. We illustrate our main theorem by considering backward shifts on the infinite-path spaces of a class of k-graphs whose shift maps *-commute. (C) 2018 Elsevier Inc. All rights reserved.
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页码：965 / 1009
页数：45
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