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arXiv · 1303.4371

Decomposition rank of UHF-absorbing C*-algebras

Hiroki Matui·Yasuhiko Sato
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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 UHF-algebra has decomposition rank at most one. Then it is proved 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. Applying this characterization, we obtain a counter-example to the Powers-Sakai conjecture.

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Hiroki Matui, Yasuhiko Sato. 2013-03-18. Decomposition rank of UHF-absorbing C*-algebras. https://doi.org/10.1215/00127094-2826908

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