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 -algebra of a row-finite graph without sinks. In particular we show that for such a path groupoid , the properties of being essential principal and the existence of a basis of -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