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- W2950347843 abstract "We consider $text{rm II}_1$ factors $L_mu(G)$ arising from 2-cocyles $mu in text{rm H}^2(G,Bbb T)$ on groups $G$ containing infinite normal subgroups $H subset G$ with the relative property $text{rm(T)}$ (i.e. $G$ {it w-rigid}). We prove that given any separable $text{rm II}_1$ factor $M$, the set of 2-cocycles $mu_{|H}in text{rm H}^2(H,Bbb T)$ with the property that $L_mu(G)$ is embeddable into $M$ is at most countable. We use this result, the relative property (T) of $Bbb Z^2 subset Bbb Z^2 rtimes Gamma$ for $Gamma subset SL(2,Bbb Z)$ non-amenable and the fact that every cocycle $mu_alpha in {text{rm H}}^2(Bbb Z^2,Bbb T)simeq Bbb T$ extends to a cocycle on $Bbb Z^2 rtimes SL(2,Bbb Z)$, to show that the one parameter family of II$_1$ factors $M_alpha(Gamma)=L_{mu_{alpha}}(Bbb Z^2 rtimes Gamma)$, $alpha in Bbb T$, are mutually non-isomorphic, modulo countable sets, and cannot all be embedded into the same separable II$_1$ factor. Other examples and applications are discussed." @default.
- W2950347843 created "2019-06-27" @default.
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- W2950347843 date "2004-01-14" @default.
- W2950347843 modified "2023-09-27" @default.
- W2950347843 title "On II$_1$ factors arising from 2-cocycles of w-rigid groups" @default.
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