Relative commutants of strongly self-absorbing C∗-algebras

Ilijas Farah, Bradd Hart, Mikael Rordam, Aaron Tikuisis

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Abstract

The relative commutant A ′ ∩A U A′∩AU of a strongly self-absorbing algebra A is indistinguishable from its ultrapower A U AU. This applies both to the case when A is the hyperfinite II 1 1 factor and to the case when it is a strongly self-absorbing C ∗ C∗-algebra. In the latter case, we prove analogous results for ℓ ∞ (A)/c 0 (A) ℓ∞(A)/c0(A) and reduced powers corresponding to other filters on N N. Examples of algebras with approximately inner flip and approximately inner half-flip are provided, showing the optimality of our results. We also prove that strongly self-absorbing algebras are smoothly classifiable, unlike the algebras with approximately inner half-flip.
Original languageEnglish
Pages (from-to)363–387
Number of pages25
JournalSelecta Mathematica
Volume23
Issue number1
Early online date29 Apr 2016
DOIs
Publication statusPublished - 1 Jan 2017

Keywords

  • central sequence algebra
  • relative commutant
  • approximately inner half-flip
  • continuous model theory
  • Strongly self-absorbing C ∗

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