论文标题
rokhlin-type特性，近似内在性和Z稳定性
Rokhlin-type properties, approximate innerness and Z-stability
论文作者
论文摘要
We establish four results concerning connections between actions on separable C*-algebras with Rokhlin-type properties and absorption of the Jiang-Su algebra Z. For actions of residually finite groups or of the reals which have finite Rokhlin dimension with commuting towers, we show that if the action of any nontrivial group element is approximately inner then the C*-algebra acted upon is Z-stable.没有关于近似内在性的假设，我们表明交叉产物在轻度假设下具有良好的可驱缘性特性。我们还为有限基团和整数的作用的广义曲折rokhlin特性和Z-吸收的奇特版本建立了类似的结果。对于具有Rokhlin属性的单个自动形态的作用，我们表明，严格弱的状况比要求自动形态的某些力量大约是内部的，即使在原始代数没有的情况下，也可以获得越野产物吸收Z。
We establish four results concerning connections between actions on separable C*-algebras with Rokhlin-type properties and absorption of the Jiang-Su algebra Z. For actions of residually finite groups or of the reals which have finite Rokhlin dimension with commuting towers, we show that if the action of any nontrivial group element is approximately inner then the C*-algebra acted upon is Z-stable. Without the assumption on approximate innerness, we show that the crossed product has good divisibility properties under mild assumptions. We also establish an analogous result for the generalized tracial Rokhlin property and tracial versions of approximate innerness and Z-absorption for actions of finite groups and of the integers. For actions of a single automorphism which have the Rokhlin property, we show that a condition which is strictly weaker than requiring that some power of the automorphism is approximately inner is sufficient to obtain that the crossed product absorbs Z even when the original algebra is not.
