The boundary quotient for algebraic dynamical systems

被引：13
|
作者：
Brownlowe, Nathan [1 ]
Stammeier, Nicolai [2 ]
机构：
[1] Univ Wollongong, Sch Math & Appl Stat, Wollongong, NSW 2522, Australia
[2] Univ Oslo, Dept Math, N-0316 Oslo, Norway
来源：
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2016年 / 438卷 / 02期
关键词：
Right LCM semigroups; Inverse semigroups; Semigroup C*-algebras; Simplicity; C-ASTERISK-ALGEBRAS; PRODUCT SYSTEMS; SEMIGROUPS;
D O I：
10.1016/j.jmaa.2016.02.015
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We introduce the notion of accurate foundation sets and the accurate refinement property for right LCM semigroups. For right LCM semigroups with this property, we derive a more explicit presentation of the boundary quotient. In the context of algebraic dynamical systems, we also analyse finiteness properties of foundation sets which lead us to a very concrete presentation. Based on Starling's recent work, we provide sharp conditions on certain algebraic dynamical systems for pure infiniteness and simplicity of their boundary quotient. (C) 2016 Elsevier Inc. All rights reserved.
引用
收藏
页码：772 / 789
页数：18
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