English

GCR and CCR Steinberg algebras

Operator Algebras 2019-08-28 v2 Rings and Algebras

Abstract

Kaplansky introduced the notions of CCR and GCR CC^*-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 CC^*-algebras. As a consequence, we classify the CCR and GCR Leavitt path algebras.

Keywords

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