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1 November 2014 Decomposition rank of UHF-absorbing C-algebras
Hiroki Matui, Yasuhiko Sato
Duke Math. J. 163(14): 2687-2708 (1 November 2014). DOI: 10.1215/00127094-2826908

Abstract

Let A be 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.

Citation

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Hiroki Matui. Yasuhiko Sato. "Decomposition rank of UHF-absorbing C-algebras." Duke Math. J. 163 (14) 2687 - 2708, 1 November 2014. https://doi.org/10.1215/00127094-2826908

Information

Published: 1 November 2014
First available in Project Euclid: 31 October 2014

zbMATH: 1317.46041
MathSciNet: MR3273581
Digital Object Identifier: 10.1215/00127094-2826908

Subjects:
Primary: 46L06, 46L35
Secondary: 46L55

Rights: Copyright © 2014 Duke University Press

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Vol.163 • No. 14 • 1 November 2014
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