On pathological properties of fixed point algebras in Kirchberg algebras
On pathological properties of fixed point algebras in Kirchberg algebras
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DOI：
10.1017/prm.2019.47
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发表时间：
2019-05
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通讯作者：
Yuhei Suzuki
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文献类型：
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作者：
Yuhei Suzuki
摘要我们研究了C*-动力系统的不动点代数如何不同于底层的C*-代数。对任意正合群Γ和任意无限群Λ，构造了Λ在Cuntz代数ε2上的外作用，ε 2的不动点代数几乎等于约化群C*-代数${\rmC}_{\rmr}^*（\Gamma）$.此外，我们还证明了任何无限群在所有不动点代数不满足完全有界逼近性质的基希贝格代数上都允许外作用。
Abstract We investigate how the fixed point algebra of a C*-dynamical system can differ from the underlying C*-algebra. For any exact group Γ and any infinite group Λ, we construct an outer action of Λ on the Cuntz algebra 𝒪2 whose fixed point algebra is almost equal to the reduced group C*-algebra ${\rm C}_{\rm r}^* (\Gamma)$. Moreover, we show that every infinite group admits outer actions on all Kirchberg algebras whose fixed point algebras fail the completely bounded approximation property.