There is no separable universal II_1-factor

Details There is no separable universal II_1-factor There is no separable universal II_1-factor

2002-10-27

arxiv.org/abs/math/0210411v2

Mathematics

Operator Algebras

4 pages. Largely revised to include an account for the construction of uncountably many simple T groups

Scientific paper

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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