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 |
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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