GCR and CCR Steinberg Algebras
Canadian journal of mathematics, Tome 72 (2020) no. 6, pp. 1581-1606
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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.
Clark, Lisa O.; Steinberg, Benjamin; Wyk, Daniel W. van. GCR and CCR Steinberg Algebras. Canadian journal of mathematics, Tome 72 (2020) no. 6, pp. 1581-1606. doi: 10.4153/S0008414X19000415
@article{10_4153_S0008414X19000415,
author = {Clark, Lisa O. and Steinberg, Benjamin and Wyk, Daniel W. van},
title = {GCR and {CCR} {Steinberg} {Algebras}},
journal = {Canadian journal of mathematics},
pages = {1581--1606},
year = {2020},
volume = {72},
number = {6},
doi = {10.4153/S0008414X19000415},
url = {http://geodesic.mathdoc.fr/articles/10.4153/S0008414X19000415/}
}
TY - JOUR AU - Clark, Lisa O. AU - Steinberg, Benjamin AU - Wyk, Daniel W. van TI - GCR and CCR Steinberg Algebras JO - Canadian journal of mathematics PY - 2020 SP - 1581 EP - 1606 VL - 72 IS - 6 UR - http://geodesic.mathdoc.fr/articles/10.4153/S0008414X19000415/ DO - 10.4153/S0008414X19000415 ID - 10_4153_S0008414X19000415 ER -
%0 Journal Article %A Clark, Lisa O. %A Steinberg, Benjamin %A Wyk, Daniel W. van %T GCR and CCR Steinberg Algebras %J Canadian journal of mathematics %D 2020 %P 1581-1606 %V 72 %N 6 %U http://geodesic.mathdoc.fr/articles/10.4153/S0008414X19000415/ %R 10.4153/S0008414X19000415 %F 10_4153_S0008414X19000415
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