Authors: Farah, Ilijas 
Hart, Bradd
Rørdam, Mikael
Tikuisis, Aaron
Title: Relative commutants of strongly self-absorbing C*-algebras
Journal: Selecta Mathematica, New Series
Volume: 23
Issue: 1
First page: 363
Last page: 387
Issue Date: 1-Jan-2017
Rank: M21
ISSN: 1022-1824
DOI: 10.1007/s00029-016-0237-y
The relative commutant A′∩ AU of a strongly self-absorbing algebra A is indistinguishable from its ultrapower AU. This applies both to the case when A is the hyperfinite II1 factor and to the case when it is a strongly self-absorbing C ∗-algebra. In the latter case, we prove analogous results for ℓ∞(A) / c0(A) and reduced powers corresponding to other filters on 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.
Keywords: Approximately inner half-flip | Central sequence algebra | Continuous model theory | Relative commutant | Strongly self-absorbing C -algebra ∗
Publisher: Springer Link

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