$C^*$-algebras of directed graphs and group actions
$C^*$-algebras of directed graphs and group actions
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$C^*$-有向图和群动作的代数
DOI：
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发表时间：
1999
影响因子：
0.9
通讯作者：
D. Pask
中科院分区：
文献类型：
--
作者：
A. Kumjian;D. Pask
给定群 $G$ 在有向图 $E$ 上的自由作用，我们证明 $C^* (E)$（$E$ 的通用 $C^*$ 代数）通过诱导作用的叉积与 $C^* (E/G)$ 强 Morita 等价。由于每个连通图 $E$ 都可以通过自由群 $G$ 的动作表示为树 $T$ 的商，我们可以使用我们的结果来表明 $C^* (E)$ 与叉积 $C_0 (partial T ) imes G$ 强 Morita 等价，其中 $partial T$ 是与树规范相关的某个零维空间。
Given a free action of a group $G$ on a directed graph $E$ we show that the crossed product of $C^* (E)$, the universal $C^*$-algebra of $E$, by the induced action is strongly Morita equivalent to $C^* (E/G)$. Since every connected graph $E$ may be expressed as the quotient of a tree $T$ by an action of a free group $G$ we may use our results to show that $C^* (E)$ is strongly Morita equivalent to the crossed product $C_0 ( partial T ) imes G$, where $partial T$ is a certain zero-dimensional space canonically associated to the tree.