A class of C*-algebras that are prime but not primitive
Operator Algebras
2013-08-26 v2 Rings and Algebras
Abstract
We establish necessary and sufficient conditions on a (not necessarily countable) graph E for the graph C*-algebra C*(E) to be primitive. Along with a known characterization of the graphs E for which C*(E) is prime, our main result provides us with a systematic method for easily producing large classes of (necessarily nonseparable) C*-algebras that are prime but not primitive. We also compare and contrast our results with similar results for Leavitt path algebras.
Cite
@article{arxiv.1306.6669,
title = {A class of C*-algebras that are prime but not primitive},
author = {Gene Abrams and Mark Tomforde},
journal= {arXiv preprint arXiv:1306.6669},
year = {2013}
}
Comments
Version II Comments: A few typos corrected. This is the version that will be published