S. 'il-existe-un-groupè-a-un-paramètre, ? it ) d'unitaires dans M tel que ? t = Ad ? it pour tout t ? R et ?(?) = ? ? ?, alors (M, ?) peut coagir strictement extérieurement sur, ) de type II ? , o` u L(F ? ) est le facteur du groupe libre avec une infinité de générateurs

?. Si, R. Est-un-sous-groupe-dénombrable-dense-de, and ?. Si, alors (M, ?) peut coagir strictement extérieurement sur un facteur de type III 0 dont le flot des poids est donné par l

A. Les, Woods libres sont très loin d'? etre moyennables. Passons doncàdoncà l'´ etude de coactions strictement extérieures de groupes quantiques sur des facteurs moyennables (ou injectifs , selon la terminologie). On a d

A. Ce-stade, il n'est pas clair si l'implication inverse est vraie. Néanmoins ceci para??tpara??t très improbable comme on verra plus loin, importantprobì eme ouvert est de mieux comprendre quels groupes quantiques localement compacts peuvent coagir strictement extérieurement sur des facteurs moyennables

. Si-une-algèbre-de, Kac discrète a une coreprésentation fidèle dans le facteur hyperfini II 1 (en particulier , si elle est moyennable)

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