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Relative commutants of strongly self-absorbing C*-algebras

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Abstract

The relative commutant A ′ ∩A U of a strongly self-absorbing algebra A is indistinguishable from its ultrapower A U . 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 halfflip.

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