# Groupoid algebras as Cuntz-Pimsner algebras

@article{Rennie2014GroupoidAA, title={Groupoid algebras as Cuntz-Pimsner algebras}, author={Adam Graham Rennie and David I. Robertson and Aidan Sims}, journal={arXiv: Operator Algebras}, year={2014} }

We show that if $G$ is a second countable locally compact Hausdorff \'etale groupoid carrying a suitable cocycle $c:G\to\mathbb{Z}$, then the reduced $C^*$-algebra of $G$ can be realised naturally as the Cuntz-Pimsner algebra of a correspondence over the reduced $C^*$-algebra of the kernel $G_0$ of $c$. If the full and reduced $C^*$-algebras of $G_0$ coincide, we deduce that the full and reduced $C^*$-algebras of $G$ coincide. We obtain a six-term exact sequence describing the $K$-theory of $C…

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