### Abstract

Original language | English |
---|---|

Pages (from-to) | 363–387 |

Number of pages | 25 |

Journal | Selecta Mathematica |

Volume | 23 |

Issue number | 1 |

Early online date | 29 Apr 2016 |

DOIs | |

Publication status | Published - 1 Jan 2017 |

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### Keywords

- central sequence algebra
- relative commutant
- approximately inner half-flip
- continuous model theory
- Strongly self-absorbing C ∗

### Cite this

*Selecta Mathematica*,

*23*(1), 363–387. https://doi.org/10.1007/s00029-016-0237-y

**Relative commutants of strongly self-absorbing C∗-algebras.** / Farah, Ilijas; Hart, Bradd; Rordam, Mikael ; Tikuisis, Aaron.

Research output: Contribution to journal › Article

*Selecta Mathematica*, vol. 23, no. 1, pp. 363–387. https://doi.org/10.1007/s00029-016-0237-y

}

TY - JOUR

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

AU - Farah, Ilijas

AU - Hart, Bradd

AU - Rordam, Mikael

AU - Tikuisis, Aaron

PY - 2017/1/1

Y1 - 2017/1/1

N2 - The relative commutant A ′ ∩A U A′∩AU of a strongly self-absorbing algebra A is indistinguishable from its ultrapower A U AU. This applies both to the case when A is the hyperfinite II 1 1 factor and to the case when it is a strongly self-absorbing C ∗ C∗-algebra. In the latter case, we prove analogous results for ℓ ∞ (A)/c 0 (A) ℓ∞(A)/c0(A) and reduced powers corresponding to other filters on N 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 ′ ∩A U A′∩AU of a strongly self-absorbing algebra A is indistinguishable from its ultrapower A U AU. This applies both to the case when A is the hyperfinite II 1 1 factor and to the case when it is a strongly self-absorbing C ∗ C∗-algebra. In the latter case, we prove analogous results for ℓ ∞ (A)/c 0 (A) ℓ∞(A)/c0(A) and reduced powers corresponding to other filters on N 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.

KW - central sequence algebra

KW - relative commutant

KW - approximately inner half-flip

KW - continuous model theory

KW - Strongly self-absorbing C ∗

U2 - 10.1007/s00029-016-0237-y

DO - 10.1007/s00029-016-0237-y

M3 - Article

VL - 23

SP - 363

EP - 387

JO - Selecta Mathematica

JF - Selecta Mathematica

SN - 1022-1824

IS - 1

ER -