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On pathological properties of fixed point algebras in Kirchberg algebras
Proceedings of the Royal Society of Edinburgh Section A: Mathematics ( IF 1.3 ) Pub Date : 2019-09-20 , DOI: 10.1017/prm.2019.47
Yuhei Suzuki

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.

中文翻译:

论Kirchberg代数中不动点代数的病理性质

我们研究了 C*-动态系统的不动点代数与基础 C*-代数有何不同。对于任何精确群 Γ 和任何无限群 Λ,我们在 Cuntz 代数 𝒪 上构造 Λ 的外作用2其不动点代数几乎等于约化群 C*-代数${\rm C}_{\rm r}^* (\Gamma)$. 此外,我们证明了每个无限群都承认在其不动点代数不满足完全有界近似属性的所有 Kirchberg 代数上的外部作用。
更新日期:2019-09-20
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