# A dichotomy for groupoid $\text{C}^{\ast }$ -algebras

@article{Rainone2017ADF, title={A dichotomy for groupoid \$\text\{C\}^\{\ast \}\$ -algebras}, author={Timothy Rainone and Aidan Sims}, journal={Ergodic Theory and Dynamical Systems}, year={2017}, volume={40}, pages={521 - 563} }

We study the finite versus infinite nature of C $^{\ast }$ -algebras arising from étale groupoids. For an ample groupoid $G$ , we relate infiniteness of the reduced C $^{\ast }$ -algebra $\text{C}_{r}^{\ast }(G)$ to notions of paradoxicality of a K-theoretic flavor. We construct a pre-ordered abelian monoid $S(G)$ which generalizes the type semigroup introduced by Rørdam and Sierakowski for totally disconnected discrete transformation groups. This monoid characterizes the finite/infinite nature…

## 14 Citations

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