We define a groupoid from a labelled space and show that it is isomorphic to the tight groupoid arising from an inverse semigroup associated with the labelled space. We then define a local homeomorphism on the tight spectrum that is a generalization of the shift map for graphs, and show that the defined groupoid is isomorphic to the Renault-Deaconu groupoid for this local homeomorphism. Finally, we show that the C*-algebra of this groupoid is isomorphic to the C*-algebra of the labelled space as introduced by Bates and Pask.

中文翻译：

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标记空间的 C*-代数的群群模型

我们从标记空间定义了一个 groupoid，并表明它与由与标记空间相关联的逆半群产生的紧 groupoid 同构。然后，我们在紧谱上定义了一个局部同胚，它是图的移位映射的推广，并表明定义的群群与该局部同胚的 Renault-Deaconu 群群同构。最后，我们证明了这个 groupoid 的 C*-代数与 Bates 和 Pask 引入的标记空间的 C*-代数同构。