UHF-slicing and classification of nuclear C*-algebras
UHF-slicing and classification of nuclear C*-algebras
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DOI：
10.1142/s1793525314500198
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发表时间：
2013-07
影响因子：
0.8
通讯作者：
Karen R. Strung;W. Winter
中科院分区：
文献类型：
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作者：
Karen R. Strung;W. Winter
本文证明了某些简单局部递归次齐次（RSH）C*-代数在用泛UHF代数张紧后是迹近似区间代数。这涉及到局部RSH代数结构的线性代数编码，允许我们找到一条穿过代数的路径，它看起来像[0，1]的离散版本，并耗尽了大部分代数。我们产生一个实际的副本的间隔，并使用C*-代数张量与UHF代数的属性移动诚实的间隔下的离散版本。从我们的主要结果可以看出，这样的C*-代数可由Elliott不变量分类。我们的定理要求在K 0-群上诱导出相同态的迹态的个数为1/2;特别是我们不要求投影分离迹态。我们应用我们的结果对Elliott构造的C*-代数的一些例子进行了分类，以穷尽不变量。我们也给出了另一种方法来分类的例子林和Matui的C*-代数的最小动力系统。这样，我们的结果可以被视为第一步，消除要求投影分离tracial状态的分类定理C*-代数的最小动力系统的汤姆斯和第二命名的作者。
In this paper we show that certain simple locally recursive subhomogeneous (RSH) C*-algebras are tracially approximately interval algebras after tensoring with the universal UHF algebra. This involves a linear algebraic encoding of the structure of the local RSH algebra allowing us to find a path through the algebra which looks like a discrete version of [0, 1] and exhausts most of the algebra. We produce an actual copy of the interval and use properties of C*-algebras tensored with UHF algebras to move the honest interval underneath the discrete version. It follows from our main result that such C*-algebras are classifiable by Elliott invariants. Our theorem requires finitely many tracial states that all induce the same state on the K0-group; in particular we do not require that projections separate tracial states. We apply our results to classify some examples of C*-algebras constructed by Elliott to exhaust the invariant. We also give an alternative way to classify examples of Lin and Matui of C*-algebras of minimal dynamical systems. In this way our result can be viewed as a first step towards removing the requirement that projections separate tracial states in the classification theorem for C*-algebras of minimal dynamical systems given by Toms and the second named author.