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GCR and CCR Steinberg Algebras
- Part of
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- Journal:
- Canadian Journal of Mathematics / Volume 72 / Issue 6 / December 2020
- Published online by Cambridge University Press:
- 23 August 2019, pp. 1581-1606
- Print publication:
- December 2020
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- Article
- Export citation
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Kaplansky introduced the notions of CCR and GCR
$C^{\ast }$-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 
$C^{\ast }$-algebras. As a consequence, we classify the CCR and GCR Leavitt path algebras.
