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continuous fields of C*-algebras — 1 results found.

      
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On AF embeddability of continuous fields
C. R. Math. Rep. Acad. Sci. Canada Vol. 31 (1) 2009, pp. 16–19
Marius Dadarlat (Received: 2008/12/18)

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Let \(A\) be a separable and exact \(C^*\)-algebra which is a continuous field of \(C^*\)-algebras over a connected, locally connected, compact metrizable space. If at least one of the fibers of \(A\) is AF embeddable, then so is \(A\). As an application we show that if \(G\) is a central extension of an amenable and residually finite discrete group by \(\mathbb{Z}^n\), then the \(C^*\)-algebra of \(G\) is AF embeddable.

Soit A une \(C^*\)-algèbre séparable et exacte qui est un champ continu de \(C^*\)-algèbres sur un espace connexe, localement connexe, compact et metrizable. Si au moins l’une des fibres de \(A\) est embeddable dans une AF algèbre donc la \(C^*\)-algèbre \(A\) est aussi. Comme application, nous montrons que si \(G\) est une extension centrale d’un groupe discret amenable et résiduellement fini par le groupe \(\mathbb{Z}^n\), alors la \(C^*\)-algèbre de \(G\) est embeddable dans une AF algèbre.

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