Groupoid Models for the C*-Algebra of Labelled Spaces

  • Giuliano Boava
  • Gilles G. de CastroEmail author
  • Fernando de L. Mortari


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.


C*-algebra Labelled space Groupoid 

Mathematics Subject Classification

Primary 46L55 Secondary 20M18 05C20 05C78 



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Copyright information

© Sociedade Brasileira de Matemática 2019

Authors and Affiliations

  1. 1.Departamento de MatemáticaUniversidade Federal de Santa CatarinaFlorianópolisBrazil

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