Relative commutants of strongly self-absorbing C*-algebras

TY - JOUR

T1 - Relative commutants of strongly self-absorbing C*-algebras

AU - Farah, Ilijas

AU - Hart, Bradd

AU - Rørdam, Mikael

AU - Tikuisis, Aaron

PY - 2017/1/1

Y1 - 2017/1/1

N2 - 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.

AB - 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.

U2 - 10.1007/s00029-016-0237-y

DO - 10.1007/s00029-016-0237-y

M3 - Journal article

SN - 1022-1824

VL - 23

SP - 363

EP - 387

JO - Selecta Mathematica

JF - Selecta Mathematica

IS - 1

ER -