English

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

Operator Algebras 2019-07-12 v1

Abstract

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

Keywords

Cite

@article{arxiv.1907.05215,
  title  = {Pure infiniteness and paradoxicality for graph $C^*$-algebras},
  author = {Francesca Arici and Baukje Debets and Karen R. Strung},
  journal= {arXiv preprint arXiv:1907.05215},
  year   = {2019}
}

Comments

12 pages