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Crossed products and MF algebras. (English) Zbl 1357.46047

The authors prove that the crossed product \(\mathscr{A}\rtimes_\alpha G\) of a unital finitely generated MF algebra \(\mathscr{A}\) by a discrete finitely generated amenable residually finite group \(G\) is an MF algebra, provided that the action \(\alpha\) is almost periodic. This generalizes a result of D. Hadwin and J.-H. Shen [Int. J. Math. 21, No. 10, 1239–1266 (2010; Zbl 1213.46055)]. They also construct two examples of crossed product \(C^*\)-algebras whose Brown-Douglas-Fillmore extension semigroups are not groups.

MSC:

46L05 General theory of \(C^*\)-algebras
46L55 Noncommutative dynamical systems

Citations:

Zbl 1213.46055
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