论文标题
部分c*dynamics和rokhlin维度
Partial C*-dynamics and Rokhlin dimension
论文作者
论文摘要
我们为有限群体的部分行动开发了Rokhlin维度的概念，从而扩展了全球系统的良好理论。部分设置表现出对全球行动无法期望的现象，这通常是由于几乎所有对有限群体行动的争论完全分解了部分系统的事实。例如，固定点代数和交叉产品总体上不相同，并且通常没有矩阵超过$ a $的跨产品$ a \ rtimes g $的本地近似。通过使用有限群体的部分作用的分解论点，我们表明，通过形成跨产品的形成，包括有限稳定等级，有限的核维度以及吸收强烈自我填充的$ C^*$ - 代数。对于与Rokhlin财产的部分行动，也保留了AF-Algebra。即使在全球案例中，我们的一些结果也是新的。 我们还研究了全球性行动的Rokhlin维度：虽然它与全球化的Rokhlin维度有所不同，但我们表明他们同意系数代数是否是UNITAL。对于在有限覆盖维度空间上的拓扑部分作用，我们表明，Rokhlin维度的有限性等同于Freeness，因此提供了我们理论适用的大量示例。
We develop the notion of Rokhlin dimension for partial actions of finite groups, extending the well-established theory for global systems. The partial setting exhibits phenomena that cannot be expected for global actions, usually stemming from the fact that virtually all averaging arguments for finite group actions completely break down for partial systems. For example, fixed point algebra and crossed product are not in general Morita equivalent, and there is in general no local approximation of the crossed product $A\rtimes G$ by matrices over $A$. By using decomposition arguments for partial actions of finite groups, we show that a number of structural properties are preserved by formation of crossed products, including finite stable rank, finite nuclear dimension, and absorption of a strongly self-absorbing $C^*$-algebra. For partial actions with the Rokhlin property, being an AF-algebra is also preserved. Some of our results are new even in the global case. We also study the Rokhlin dimension of globalizable actions: while in general it differs from the Rokhlin dimension of its globalization, we show that they agree if the coefficient algebra is unital. For topological partial actions on spaces of finite covering dimension, we show that finiteness of the Rokhlin dimension is equivalent to freeness, thus providing a large class of examples to which our theory applies.
