GCR and CCR Steinberg algebras
Operator Algebras
2019-08-28 v2 Rings and Algebras
Abstract
Kaplansky introduced the notions of CCR and GCR -algebras because they have a tractable representation theory. Many years later, he introduced the notions of CCR and GCR rings. In this paper we characterize when the algebra of an ample groupoid over a field is CCR and GCR. The results turn out to be exact analogues of the corresponding characterization of locally compact groupoids with CCR and GCR -algebras. As a consequence, we classify the CCR and GCR Leavitt path algebras.
Cite
@article{arxiv.1901.06056,
title = {GCR and CCR Steinberg algebras},
author = {Lisa Orloff Clark and Benjamin Steinberg and Daniel W van Wyk},
journal= {arXiv preprint arXiv:1901.06056},
year = {2019}
}
Comments
Minor revisions made based on the referee reports