Cartan subalgebras in C*-algebras. Existence and uniqueness
Cartan subalgebras in C*-algebras. Existence and uniqueness
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C* 代数中的嘉当子代数。
DOI：
10.1090/tran/7654
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发表时间：
2019
影响因子：
1.3
通讯作者：
Li X
中科院分区：
文献类型：
--
作者：
Li X
我们开始了C*-代数中Cartan子代数的研究，特别关注了存在性和唯一性问题。对于齐次C*-代数，这些问题可以用纤维束理论进行系统的分析。对于群C*-代数，虽然我们能够在许多连通李群的C*-代数中找到Cartan子代数，但也存在（离散）群，例如非阿贝尔自由群，其约简群C*-代数没有Cartan子代数。此外，我们还证明了对于可分类C*-代数，Cartan子代数的唯一性通常是不成立的。然而，在某些情况下，存在着不同的Cartan子代数，例如在核均匀Roe代数中。参考文献
We initiate the study of Cartan subalgebras in C*-algebras, with a particular focus on existence and uniqueness questions. For homogeneous C*-algebras, these questions can be analyzed systematically using the theory of fiber bundles. For group C*-algebras, while we are able to find Cartan subalgebras in C*-algebras of many connected Lie groups, there are classes of (discrete) groups, for instance non-abelian free groups, whose reduced group C*-algebras do not have any Cartan subalgebras. Moreover, we show that uniqueness of Cartan subalgebras usually fails for classifiable C*-algebras. However, distinguished Cartan subalgebras exist in some cases, for instance in nuclear uniform Roe algebras. References