Uniqueness theorems for topological higher-rank graph C*-algebras
Operator Algebras
2012-09-11 v3
Abstract
We consider the boundary-path groupoids of topological higher-rank graphs. We show that the all such groupoids are topologically amenable. We deduce that the C*-algebras of topological higher-rank graphs are nuclear and prove versions of the gauge-invariant uniqueness theorem and the Cuntz-Krieger uniqueness theorem. We then provide a necessary and sufficient condition for simplicity of a topological higher-rank graph C*-algebra, and a condition under which it is also purely infinite.
Keywords
Cite
@article{arxiv.0906.0829,
title = {Uniqueness theorems for topological higher-rank graph C*-algebras},
author = {Jean N. Renault and Aidan Sims and Dana P. Williams and Trent Yeend},
journal= {arXiv preprint arXiv:0906.0829},
year = {2012}
}
Comments
Comments for version 3: proofs of uniqueness theorems substantially streamlined and errors in the proof of amenability corrected. New results on simplicity and pure infinite added. 15 pages