There is no separable universal 𝐼𝐼₁-factor
N Ozawa - Proceedings of the American Mathematical Society, 2004 - ams.org
Proceedings of the American Mathematical Society, 2004•ams.org
Gromov constructed uncountably many pairwise nonisomorphic discrete groups with
Kazhdan's property $\mathrm {(T)} $. We will show that no separable $\mathrm {II} _1 $-
factor can contain all these groups in its unitary group. In particular, no separable $\mathrm
{II} _1 $-factor can contain all separable $\mathrm {II} _1 $-factors in it. We also show that the
full group $ C^* $-algebras of some of these groups fail the lifting property. References
Kazhdan's property $\mathrm {(T)} $. We will show that no separable $\mathrm {II} _1 $-
factor can contain all these groups in its unitary group. In particular, no separable $\mathrm
{II} _1 $-factor can contain all separable $\mathrm {II} _1 $-factors in it. We also show that the
full group $ C^* $-algebras of some of these groups fail the lifting property. References
Abstract
Gromov constructed uncountably many pairwise nonisomorphic discrete groups with Kazhdan’s property . We will show that no separable -factor can contain all these groups in its unitary group. In particular, no separable -factor can contain all separable -factors in it. We also show that the full group -algebras of some of these groups fail the lifting property. References
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