Relative commutants of strongly self-absorbing 1"> \(\mathrm {C}^*\) -algebras

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• 作者：Ilijas Farah ; Bradd Hart ; Mikael Rørdam ; Aaron Tikuisis
• 关键词：Central sequence algebra ; Relative commutant ; Strongly self ; absorbing C\(^{*}\) ; algebra ; Approximately inner half ; flip ; Continuous model theory
• 刊名：Selecta Mathematica
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：23
• 期：1
• 页码：363-387
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics, general;
• 出版者：Springer International Publishing
• ISSN：1420-9020
• 卷排序：23

文摘

The relative commutant \(A^{\prime }\cap A^{\mathcal U}\) of a strongly self-absorbing algebra A is indistinguishable from its ultrapower \(A^{\mathcal U}\). This applies both to the case when A is the hyperfinite II\(_1\) factor and to the case when it is a strongly self-absorbing \(\mathrm {C}^*\)-algebra. In the latter case, we prove analogous results for \(\ell _\infty (A)/c_0(A)\) and reduced powers corresponding to other filters on \({\mathbb N}\). 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.