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arXiv · 1907.05215

Pure infiniteness and paradoxicality for graph $C^*$-algebras

Francesca Arici·Baukje Debets·Karen R. Strung
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Abstract

We obtain necessary and sufficient conditions for pure infiniteness of the path groupoid $C^*$-algebra of a row-finite graph without sinks. In particular we show that for such a path groupoid $\mathcal{G}_E$, the properties of being essential principal and the existence of a basis of $(\mathcal{G}_E^a, 2, 1)$-paradoxical sets for the topology are not only sufficient, but also necessary.

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Francesca Arici, Baukje Debets, Karen R. Strung. 2019-07-11. Pure infiniteness and paradoxicality for graph $C^*$-algebras. https://arxiv.org/abs/1907.05215

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