There is no separable universal II_1-factor

By Nathanial P. Brown Narutaka Ozawa. 2002

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Gromov constructed uncountably many pairwise non-isomorphic discrete groups with Kazhdan's property (T). We will show that no separable II_1-factor can contain all these groups in its unitary group. In particular, no separable II_1-factor can contain all separable II_1-factors in it. We also show that the full group C*-algebras of some of these groups fail the lifting property.

View Paper: https://www.semanticscholar.org/paper/b009177697c6ee0772f4b093c701329bcc902ea8

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Citations in the corpus

• Model theory of operator algebras III: elementary equivalence and II1 factors (2011, result): “This contrasts with Ozawa’s theorem that there is no universal object for separable II1 factors [42].”
• Amenable actions, free products and a fixed point property (2005, background): “2 applies in particular to infinite simple Kazhdan groups; we point out that such groups do indeed exist, as follows from the work of Gromov [16] and Ol′shanskĭı [25] on quotients of hyperbolic groups (see [26] for precise references).”