Uniform Property G
Uniform Property G
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统一属性G
DOI：
10.1093/imrn/rnaa282
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发表时间：
2022
影响因子：
1
通讯作者：
Castillejos J
中科院分区：
文献类型：
--
作者：
Castillejos J
我们进一步研究的概念，统一的属性为代数介绍了我们的联合工作与冬季。除了获得表征的精神，Dixlane的工作中心序列在IIfactors，我们建立了等价的一致性，一个合适的统一版本的McDuff的属性代数，并存在补充分区的单位可分核代数没有有限维表示和一个紧凑的（非空）tracial状态空间。因此，对于Toms-Winter猜想中的-代数，严格比较和一致性的结合等价于Jiang-Su稳定性.我们还展示了如何将这些想法与Matui-Sato相结合，通过嵌入技术来简化Winter的分类。
We further examine the concept of uniform propertyfor-algebras introduced in our joint work with Winter. In addition to obtaining characterisations in the spirit of Dixmier’s work on central sequences in IIfactors, we establish the equivalence of uniform property, a suitable uniform version of McDuff’s property for-algebras, and the existence of complemented partitions of unity for separable nuclear-algebras with no finite dimensional representations and a compact (non-empty) tracial state space. As a consequence, for-algebras as in the Toms–Winter conjecture, the combination of strict comparison and uniform propertyis equivalent to Jiang–Su stability. We also show how these ideas can be combined with those of Matui–Sato to streamline Winter’s classification by embeddings technique.