Full groups of Cantor minimal systems
Full groups of Cantor minimal systems
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完整的康托最小系统群
DOI：
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发表时间：
1999
期刊：
影响因子：
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通讯作者：
Christian F. Skau
中科院分区：
文献类型：
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作者：
T. Giordano;I. Putnam;Christian F. Skau
我们将不同类型的全群与康托极小系统联系起来。我们展示了这些不同的群体（作为抽象群体）是完全不变的轨道等价，强轨道等价和翻转共轭，分别。此外，我们引入了一个群同态，所谓的模映射，从各种满群的正规化子到（有序）K 0-群的自同构群，这是与康托极小系统。我们展示了如何这反过来是相关的associatedC*-交叉产品的自同构。我们的结果是类似物的拓扑动力学设置的Dye，Connes-Krieger和Hamachi-Osikawa在可测动力学的结果。
We associate different types of full groups to Cantor minimal systems. We show how these various groups (as abstract groups) are complete invariants for orbit equivalence, strong orbit equivalence and flip conjugacy, respectively. Furthermore, we introduce a group homomorphism, the socalled mod map, from the normalizers of the various full groups to the automorphism groups of the (ordered)K0-groups, which are associated to the Cantor minimal systems. We show how this in turn is related to the automorphisms of the associatedC*-crossed products. Our results are analogues in the topological dynamical setting of results obtained by Dye, Connes-Krieger and Hamachi-Osikawa in measurable dynamics.