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- W4214528538 abstract "The question of which separable C*-algebras have abelian central sequence algebras was raised and studied by Phillips ([17]) and Ando-Kirchberg ([2]). 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. 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." @default.
- W4214528538 created "2022-03-02" @default.
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- W4214528538 date "2022-06-01" @default.
- W4214528538 modified "2023-09-26" @default.
- W4214528538 title "Commutativity of central sequence algebras" @default.
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- W4214528538 doi "https://doi.org/10.1016/j.aim.2022.108262" @default.
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