Decomposition rank of UHF-absorbing c* -algebras

Hiroki Matui, Yasuhiko Sato

Research output: Contribution to journalArticlepeer-review

50 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)2687-2708
Number of pages22
JournalDuke Mathematical Journal
Volume163
Issue number14
DOIs
Publication statusPublished - 2014

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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