Tracially AF *-algebras
Tracially AF *-algebras
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DOI：
10.1090/s0002-9947-00-02680-5
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发表时间：
2000-09
影响因子：
1.3
通讯作者：
Huaxin Lin
中科院分区：
文献类型：
--
作者：
Huaxin Lin
受S.在Popa和核代数分类理论的基础上，我们引入了一类-代数，称之为迹近似有限维（TAF）。TAF-代数一般不是AF-代数，但它的“大”部分可以用有限维子代数来近似。证明了TAF单代数是拟对角的，并且有真实的秩零，稳定秩一和弱不穿孔群。迄今为止，根据理论数据分类的具有弱不穿孔群的真实的秩为零、稳定秩为一的核单代数都是TAF。我们给出了非核单TAF-代数的例子。给出了有单位元的核可分拟对角代数是TAF的一个充分条件。主要结果包括单有理AF-代数的一个刻画。本文证明了满足泛系数定理且具有和的可分核单TAF-代数同构于具有相同理论的单AF-代数。引用
Inspired by a paper of S. Popa and the classification theory of nuclear-algebras, we introduce a class of-algebras which we call tracially approximately finite dimensional (TAF). A TAF-algebra is not an AF-algebra in general, but a “large” part of it can be approximated by finite dimensional subalgebras. We show that if a unital simple-algebra is TAF then it is quasidiagonal, and has real rank zero, stable rank one and weakly unperforated-group. All nuclear simple-algebras of real rank zero, stable rank one, with weakly unperforated-group classified so far by their-theoretical data are TAF. We provide examples of nonnuclear simple TAF-algebras. A sufficient condition for unital nuclear separable quasidiagonal-algebras to be TAF is also given. The main results include a characterization of simple rational AF-algebras. We show that a separable nuclear simple TAF-algebrasatisfying the Universal Coefficient Theorem and havingandis isomorphic to a simple AF-algebra with the same-theory. References