|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||Abstract:||
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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