Group C*-algebras as decreasing intersection of nuclear C*-algebras
Group C*-algebras as decreasing intersection of nuclear C*-algebras
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DOI：
10.1353/ajm.2017.0018
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发表时间：
2014-10
影响因子：
1.7
通讯作者：
Yuhei Suzuki
中科院分区：
文献类型：
--
作者：
Yuhei Suzuki
证明了对任意正合离散群$Gamma$，在约化群$\rMC-代数与群von Neumann代数与一致Roe代数的交之间存在一个中间代数，它可实现为Cuntz代数的同构递减序列的交.特别地，当$\Gamma$具有AP(逼近性质)时，用这种方法实现了约化群$\rmC}^\ast$-代数。我们还研究了约化自由群Ast$-代数的扩张，证明了任何稳定的可分核Ast$-代数对它的任何精确吸收扩张或单位吸收扩张都是这样实现的。
We prove that for every exact discrete group $\Gamma$, there is an intermediate ${\rm C}^\ast$-algebra between the reduced group ${\rm C}^\ast$-algebra and the intersection of the group von Neumann algebra and the uniform Roe algebra which is realized as the intersection of a decreasing sequence of isomorphs of the Cuntz algebra ${\cal O}_2$. In particular, when $\Gamma$ has the AP (approximation property), the reduced group ${\rm C}^\ast$-algebra is realized in this way. We also study extensions of the reduced free group ${\rm C}^\ast$-algebras and show that any exact absorbing or unital absorbing extension of it by any stable separable nuclear ${\rm C}^\ast$-algebra is realized in this way.