中心序列代数的交换性
Commutativity of central sequence algebras
摘要：
Phillips（[Ph 88]）和Ando-Kirchberg（[AK 14]）提出并研究了哪些可分C* 代数-代数具有交换中心序列代数的问题。本文给出了可分C* 代数$A$有交换中心序列代数的充要条件是A满足Fell条件。此外，我们引入了一个更高的维类似的费尔的条件，并表明，它完全刻画了次齐性的中心序列代数。相反，我们证明了任何非平凡的紧算子扩张不仅具有非交换的，而且甚至没有剩余的I型中心序列代数。特别是它的中心序列代数不是I型的，也不是剩余有限维的。我们的技巧广泛地利用了C* 代数中幂零元的性质。
英文摘要：
The question of which separable C*-algebras have abelian central sequence algebras was raised and studied by Phillips ([Ph88]) and Ando-Kirchberg ([AK14]). In this paper we give a complete answer to their question: A separable C*-algebra $A$ has abelian central sequence algebra if and only if A satisfies Fell's condition. Moreover, we introduce a higher-dimensional analogue of Fell's condition and show that it completely characterizes subhomogeneity of central sequence algebras. In contrast, we show that any non-trivial extension by compact operators has not only non-abelian but not even residually type I central sequence algebra. In particular its central sequence algebra is not type I and not residually finite-dimensional (RFD). Our techniques extensively use properties of nilpotent elements in C*-algebras.
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