Relative commutants of strongly self-absorbing C*-algebras

2015/02/18 by Ilijas Farah, Bradd Hart, Farah, Ilijas +5
Mathematics · #03C98 #46L05 #Advanced Banach Space Theory #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Logic (math.LO) #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.1502.05228

openalex publication_date 2015/02/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 \bf 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.

Citations

• Countable saturation of corona algebras
• Logic and operator algebras

Related

• Strongly self-absorbing C*-algebras
• Computably strongly self-absorbing C*-algebras
• The relative commutant of separable C*-algebras of real rank zero
• Permutations of Strongly Self-Absorbing C*-algebras
• Strongly self-absorbing C*-algebras are Z-stable