Groupoid Models for the C*-Algebra of Labelled Spaces
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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.
KeywordsC*-algebra Labelled space Groupoid
Mathematics Subject ClassificationPrimary 46L55 Secondary 20M18 05C20 05C78
- Raeburn, I: Graph algebras, volume 103 of CBMS Regional Conference Series in Mathematics. Published for the Conference Board of the Mathematical Sciences, Washington, DC; by the American Mathematical Society, Providence, RI (2005)Google Scholar
- Renault, J: Cuntz-like algebras. In Operator theoretical methods (Timişoara, 1998), pages 371–386. Theta Found., Bucharest (2000)Google Scholar