# 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}
}
• Published 14 July 2017
• Mathematics
• Ergodic Theory and Dynamical Systems
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…
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In this paper, we study the ideal structure of reduced $C^{\ast }$ -algebras $C_{r}^{\ast }(G)$ associated to étale groupoids $G$ . In particular, we characterize when there is a one-to-one
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