Residually finite actions and crossed products

被引：17
作者：
Kerr, David [1 ]
Nowak, Piotr W. [1 ]
机构：
[1] Texas A&M Univ, Dept Math, College Stn, TX 77843 USA
来源：
ERGODIC THEORY AND DYNAMICAL SYSTEMS | 2012年 / 32卷
基金：
美国国家科学基金会;
关键词：
C-STAR-ALGEBRAS; ASTERISK-ALGEBRAS; PRIMITIVE-IDEALS; QUASIDIAGONALITY; MATRICES; HOMOTOPY;
D O I：
10.1017/S0143385711000575
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We study a notion of residual finiteness for continuous actions of discrete groups on compact Hausdorff spaces and how it relates to the existence of norm microstates for the reduced crossed product. Our main result asserts that an action of a free group on a zero-dimensional compact metrizable space is residually finite if and only if its reduced crossed product admits norm microstates, i.e., is an MF algebra.
引用
收藏
页码：1585 / 1614
页数：30
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