论文标题
在分离图C*-ergebras上的组的免费动作
Free actions of groups on separated graph C*-algebras
论文作者
论文摘要
在本文中，我们研究了在分离图及其\ cstar {}代数上的组的自由作用，从而推广了涉及普通（有向）图的先前结果。 我们证明了通过（Orbit）通过组标记函数的（Orbit）分离图的偏斜产物在分离的图上表征的分离图的总定理的版本。此外，我们将与这些偏斜产物相关的C* - 代数描述为杂交产品，通过图表上的标记函数的某些共同。我们的结果涉及分离图的完整和减少的C* - 代数。 为了证明我们的主要结果，我们使用了几种涉及分离图的C* - 代数及其结构定义的某些规范条件期望的技术，它们是普通图C*-Algebras的合并的免费产品。此外，我们描述了与出现标记函数的共同体相关的Fell Bundles。作为我们结果的副产品，我们推断出分离图的\ cstar {}代数总是在其边缘上的自由组上有一个规范的跌落束结构。
In this paper we study free actions of groups on separated graphs and their \cstar{}algebras, generalizing previous results involving ordinary (directed) graphs. We prove a version of the Gross-Tucker Theorem for separated graphs yielding a characterization of free actions on separated graphs via a skew product of the (orbit) separated graph by a group labeling function. Moreover, we describe the C*-algebras associated to these skew products as crossed products by certain coactions coming from the labeling function on the graph. Our results deal with both the full and the reduced C*-algebras of separated graphs. To prove our main results we use several techniques that involve certain canonical conditional expectations defined on the C*-algebras of separated graphs and their structure as amalgamated free products of ordinary graph C*-algebras. Moreover, we describe Fell bundles associated with the coactions of the appearing labeling functions. As a byproduct of our results, we deduce that the \cstar{}algebras of separated graphs always have a canonical Fell bundle structure over the free group on their edges.
