THE PURE EXTENSION PROPERTY FOR DISCRETE CROSSED PRODUCTS

被引：0

作者：

Zarikian, Vrej ^{[1
]}

机构：

[1] US Naval Acad, Dept Math, Annapolis, MD 21402 USA

来源：

HOUSTON JOURNAL OF MATHEMATICS | 2019年 / 45卷 / 01期

关键词：

Pure state extension property; crossed product C*-algebra; free action; discrete group;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let G be a discrete group acting on a unital C*-algebra A by *-automorphisms. In this note, we show that the inclusion A subset of A sic(r)G has the pure extension property (so that every pure state on A extends uniquely to a pure state on A sic(r)G) if and only if G acts freely on (A) over cap, the spectrum of A. The same characterization holds for the inclusion A subset of A sic( )G. This generalizes what was already known for A abelian.

引用

页码：233 / 243

页数：11

共 22 条

[1] PURE STATES ON FREE GROUP C*-ALGEBRAS [J].