# Product between ultrafilters and applications to the Connes&#x27; embedding problem - Mathematics > Operator Algebras

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Abstract: In this paper we want to apply the notion of product between ultrafilters toanswer several questions which arise around the Connes- embedding problem. Forinstance, we will give a simplification and generalization of a theorem byRadulescu; we will prove that ultraproduct of hyperlinear groups is stillhyperlinear and consequently the von Neumann algebra of the free group withuncountable many generators is embeddable into $R^{\omega}$. This follows alsofrom a general construction that allows, starting from an hyperlinear group, tofind a family of hyperlinear groups. We will introduce the notion ofhyperlinear pair and we will use it to give some other characterizations ofhyperlinearity. We will prove also that the cross product of a hyperlineargroup via a profinite action is embeddable into $R^{\omega}$.

Autor: V. Capraro, L. Paunescu

Fuente: https://arxiv.org/