Relative commutants of strongly self-absorbing C∗-algebras

Ilijas Farah ^[1] ; Bradd Har ^[2] ; Mikael Rørdam ^[3] ; Aaron Tikuisis ^[4]
1. [1] York University (Canadá)
  
  York University (Canadá)
  
  Canadá
2. [2] McMaster University
  
  McMaster University
  
  Canadá
3. [3] University of Copenhagen
  
  University of Copenhagen
  
  Dinamarca
4. [4] University of Aberdeen
  
  University of Aberdeen
  
  Reino Unido
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Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 23, Nº. 1, 2017, págs. 363-387
Idioma: inglés
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Resumen
- 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 ∞(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.