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arXiv · 2107.01389

Topological graphs and singly generated dynamical systems

Takeshi Katsura
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Abstract

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.

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Takeshi Katsura. 2021-07-03. Topological graphs and singly generated dynamical systems. https://arxiv.org/abs/2107.01389

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