TY - JOUR

T1 - Decomposition rank of UHF-absorbing c* -algebras

AU - Matui, Hiroki

AU - Sato, Yasuhiko

N1 - Publisher Copyright:
© 2014.
Copyright:
Copyright 2018 Elsevier B.V., All rights reserved.

PY - 2014

Y1 - 2014

N2 - Let Abe a unital separable simple C*-algebra with a unique tracial state. We prove that if A is nuclear and quasidiagonal, then A tensored with the universal uniformly hyperfinite (UHF) algebra has decomposition rank at most one. We then prove that A is nuclear, quasidiagonal, and has strict comparison if and only if A has finite decomposition rank. For such A, we also give a direct proof that A tensored with a UHF algebra has tracial rank zero. Using this result, we obtain a counterexample to the Powers-Sakai conjecture.

AB - Let Abe a unital separable simple C*-algebra with a unique tracial state. We prove that if A is nuclear and quasidiagonal, then A tensored with the universal uniformly hyperfinite (UHF) algebra has decomposition rank at most one. We then prove that A is nuclear, quasidiagonal, and has strict comparison if and only if A has finite decomposition rank. For such A, we also give a direct proof that A tensored with a UHF algebra has tracial rank zero. Using this result, we obtain a counterexample to the Powers-Sakai conjecture.

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U2 - 10.1215/00127094-2826908

DO - 10.1215/00127094-2826908

M3 - Article

AN - SCOPUS:84919328092

VL - 163

SP - 2687

EP - 2708

JO - Duke Mathematical Journal

JF - Duke Mathematical Journal

SN - 0012-7094

IS - 14

ER -