Simple nuclear C∗-algebras not isomorphic to their opposites

Ilijas Farah, Ilan Hirshberg

Research output: Contribution to journalArticlepeer-review


We show that it is consistent with Zermelo-Fraenkel set theory with the axiom of choice (ZFC) that there is a simple nuclear nonseparable C-algebra, which is not isomorphic to its opposite algebra. We can furthermore guarantee that this example is an inductive limit of unital copies of the Cuntz algebra O2 or of the canonical anticommutation relations (CAR) algebra.

Original languageAmerican English
Pages (from-to)6244-6249
Number of pages6
JournalProceedings of the National Academy of Sciences of the United States of America
Issue number24
StatePublished - 13 Jun 2017


  • CC∗-algebras
  • Glimm dichotomy
  • Jensen's diamond
  • Naimark's problem
  • Opposite algebra

All Science Journal Classification (ASJC) codes

  • General

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