An intrinsic characterization of C*-simplicity
An intrinsic characterization of C*-simplicity
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C* 简单性的内在特征
DOI：
10.24033/asens.2441
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发表时间：
2015
期刊：
影响因子：
--
通讯作者：
M. Kennedy
中科院分区：
文献类型：
--
作者：
M. Kennedy
一个群称为C*-单群，如果它的约化C*-代数是单群。我们建立了一个内在的（群论）表征群与此属性。具体地说，我们证明了一个离散群是C*-单纯的当且仅当它没有非平凡的顺从一致递归子群。我们进一步证明了一个群是C*-单纯的当且仅当它满足Powers所考虑的一个平均性质。
A group is said to be C*-simple if its reduced C*-algebra is simple. We establish an intrinsic (group-theoretic) characterization of groups with this property. Specifically, we prove that a discrete group is C*-simple if and only if it has no non-trivial amenable uniformly recurrent subgroups. We further prove that a group is C*-simple if and only if it satisfies an averaging property considered by Powers.