Pure infiniteness and paradoxicality for graph $C^{\ast }$-algebras

Abstract

We obtain necessary and sufficient conditions for pure infiniteness of the path groupoid $C^{\ast }$-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.

12 pages

References in corpus (2)

• Graph inverse semigroups, groupoids and their C*-algebras
• Purely infinite $C^{\ast }$-algebras associated to étale groupoids