Relative commutants of strongly self-absorbing C*-algebras

摘要: The relative commutant $A'\cap A^{\mathcal{U}}$ of a strongly self-absorbing algebra $A$ is indistinguishable from its ultrapower $A^{\mathcal{U}}$. This applies both to the case when hyperfinite II$_1$ factor and it C*-algebra. In latter we prove analogous results for $\ell_\infty(A)/c_0(A)$ reduced powers corresponding other filters on $\bf N$. Examples algebras with approximately inner flip half-flip are provided, showing optimality our results. We also that smoothly classifiable, unlike half-flip.