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There is no separable universal II_1-factor

Narutaka Ozawa
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Abstract

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.

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Narutaka Ozawa. 2002-11-02. There is no separable universal II_1-factor. https://arxiv.org/abs/math/0210411

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