Rokhlin Dimension and C*-Dynamics
Rokhlin Dimension and C*-Dynamics
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DOI：
10.1007/s00220-014-2264-x
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发表时间：
2015-02
影响因子：
2.4
通讯作者：
Ilan Hirshberg;W. Winter;J. Zacharias
中科院分区：
文献类型：
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作者：
Ilan Hirshberg;W. Winter;J. Zacharias
提出了c *-代数上整数和有限群作用的Rokhlin维数的概念。我们的概念推广了所谓的罗克林性质，它可以被认为是罗克林维数为0。我们证明了有限的Rokhlin维数是普遍存在的，并且出现在不能期望Rokhlin性质的情况下：具有有限Rokhlin维数的性质对于稳定c *-代数的自同构是一般的，其中注意到Jiang-Su代数。此外，有限Rokhlin维数自同构的交叉积保持了核维数有限的性质，并在一个温和的附加假设下保持了稳定性。在拓扑动力学中，我们的概念可以解释为经典Rokhlin引理的拓扑版本：有限维紧化可度量空间的极小同胚产生的自同构总是具有有限的Rokhlin维数。后一个结果现已由Szabó推广到紧致可度量和有限维空间上的自由和非周期作用。
We develop the concept of Rokhlin dimension for integer and for finite group actions onC*-algebras. Our notion generalizes the so-called Rokhlin property, which can be thought of as Rokhlin dimension 0. We show that finite Rokhlin dimension is prevalent and appears in cases in which the Rokhlin property cannot be expected: the property of having finite Rokhlin dimension is generic for automorphisms of-stableC*-algebras, wheredenotes the Jiang–Su algebra. Moreover, crossed products by automorphisms with finite Rokhlin dimension preserve the property of having finite nuclear dimension, and under a mild additional hypothesis also preserve-stability. In topological dynamics our notion may be interpreted as a topological version of the classical Rokhlin lemma: automorphisms arising from minimal homeomorphisms of finite dimensional compact metrizable spaces always have finite Rokhlin dimension. The latter result has by now been generalized by Szabó to the case of free and aperiodic-actions on compact metrizable and finite dimensional spaces.