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arXiv · 1811.12754

Groupoid models for the C*-algebra of labelled spaces

Giuliano Boava·Gilles G. de Castro·Fernando de L. Mortari
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Abstract

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.

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Giuliano Boava, Gilles G. de Castro, Fernando de L. Mortari. 2018-11-30. Groupoid models for the C*-algebra of labelled spaces. https://arxiv.org/abs/1811.12754

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