Decomposition rank of UHF-absorbing C*-algebras

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.

19 pages, a counter example to the Powers-Sakai conjecture added

References in corpus (1)

• Z-stability of crossed products by strongly outer actions II

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