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arXiv · 1901.06056

GCR and CCR Steinberg algebras

Lisa Orloff Clark·Benjamin Steinberg·Daniel W van Wyk
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Abstract

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

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Lisa Orloff Clark, Benjamin Steinberg, Daniel W van Wyk. 2019-01-18. GCR and CCR Steinberg algebras. https://doi.org/10.4153/s0008414x19000415

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