Li, Weihua; Orfanos, Stefanos Crossed products and MF algebras. (English) Zbl 1357.46047 Oper. Matrices 10, No. 3, 679-689 (2016). 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. Reviewer: Pierre Clare (Hanover) MSC: 46L05 General theory of \(C^*\)-algebras 46L55 Noncommutative dynamical systems Keywords:MF algebras; crossed products; Brown-Douglas-Fillmore semigroups; amenable groups; residually finite groups Citations:Zbl 1213.46055 PDFBibTeX XMLCite \textit{W. Li} and \textit{S. Orfanos}, Oper. Matrices 10, No. 3, 679--689 (2016; Zbl 1357.46047) Full Text: DOI arXiv