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
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
收藏
页码:3087 / 3096
页数:10
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