In this paper we want to apply the notion of product between ultrafilters to answer several questions which arise around Connes' embedding problem. We shall prove that an ultraproduct of hyperlinear groups is still hyperlinear and consequently the von Neumann algebra of the free group with uncountable many generators is embeddable into Rω. This follows also from a general construction that allows, starting from an hyperlinear group, to find a family of hyperlinear groups. We shall prove also that the cross product of an hyperlinear group via a profinite action is embeddable into Rω.

Capraro, V., Paunescu, L. (2012). Product between ultrafilters and applications to Connes' embedding problem. JOURNAL OF OPERATOR THEORY, 68(1), 165-172.

Product between ultrafilters and applications to Connes' embedding problem

Capraro, V;
2012

Abstract

In this paper we want to apply the notion of product between ultrafilters to answer several questions which arise around Connes' embedding problem. We shall prove that an ultraproduct of hyperlinear groups is still hyperlinear and consequently the von Neumann algebra of the free group with uncountable many generators is embeddable into Rω. This follows also from a general construction that allows, starting from an hyperlinear group, to find a family of hyperlinear groups. We shall prove also that the cross product of an hyperlinear group via a profinite action is embeddable into Rω.
Articolo in rivista - Articolo scientifico
Connes' embedding problem; Hyperlinear groups; Product of ultrafilters
English
165
172
8
Capraro, V., Paunescu, L. (2012). Product between ultrafilters and applications to Connes' embedding problem. JOURNAL OF OPERATOR THEORY, 68(1), 165-172.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/397930
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