@article{Rennie_Robertson_Sims_2017, title={Groupoid algebras as Cuntz-Pimsner algebras}, volume={120}, url={https://www.mscand.dk/article/view/25507}, DOI={10.7146/math.scand.a-25507}, abstractNote={<p>We show that if $G$ is a second countable locally compact Hausdorff étale groupoid carrying a suitable cocycle $c\colon G\to\mathbb{Z}$, 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 $C^*_r(G)$ in terms of that of $C^*_r(G_0)$.</p>}, number={1}, journal={MATHEMATICA SCANDINAVICA}, author={Rennie, Adam and Robertson, David and Sims, Aidan}, year={2017}, month={Feb.}, pages={115–123} }