Topological graphs and singly generated dynamical systems
Topological graphs and singly generated dynamical systems
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拓扑图和单生成动力系统
DOI：
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发表时间：
2021
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通讯作者：
Takeshi Katsura
中科院分区：
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作者：
Takeshi Katsura
本文引入了给定拓扑图的对偶拓扑图的概念，并证明了它定义了一个同构于给定拓扑图的C-代数的C-代数。重复取一个对偶，再取一个投影极限，得到一个单生成动力系统，其伴随的C-代数与给定拓扑图的C-代数同构。这表明任意拓扑图的C-代数都有群胚模型。对本文所引入的相对拓扑图和部分定义拓扑图也作了类似的研究。
In this paper, we introduce the notion of a dual topological graph of a given topological graph, and show that it defines a C∗-algebra isomorphic to the C∗-algebra of the given one. Repeating to take a dual, and taking a projective limit, we get a singly generated dynamical system with which the associate C∗-algebra is isomorphic to the C∗-algebra of the given topological graph. This shows that a C∗-algebra of an arbitrary topoloical graph has a groupoid model. Similar investigation are done for relative topoloical graphs and partially defined topoloical graphs which are introduced in this paper.