On pathological properties of fixed point algebras in Kirchberg algebras

被引：2

作者：

Suzuki, Yuhei ^{[1
]}

机构：

[1] Nagoya Univ, Grad Sch Math, Chikusa Ku, Nagoya, Aichi 4648602, Japan

来源：

PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS | 2020年 / 150卷 / 06期

关键词：

Fixed point algebras; nuclearity; non-commutative dynamical systems; C-ASTERISK-ALGEBRAS; REDUCED CROSSED-PRODUCTS; PURE STATE-SPACE; NUCLEAR; CLASSIFICATION; AUTOMORPHISMS; HOMOGENEITY;

D O I：

10.1017/prm.2019.47

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We investigate how the fixed point algebra of a C*-dynamical system can differ from the underlying C*-algebra. For any exact group Gamma and any infinite group Lambda, we construct an outer action of Lambda on the Cuntz algebra O-2 whose fixed point algebra is almost equal to the reduced group C*-algebra C-r(*)(Gamma). Moreover, we show that every infinite group admits outer actions on all Kirchberg algebras whose fixed point algebras fail the completely bounded approximation property.

引用

页码：3087 / 3096

页数：10

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