There is no separable universal II_1-factor
Operator Algebras
2007-05-23 v2
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.
Keywords
Cite
@article{arxiv.math/0210411,
title = {There is no separable universal II_1-factor},
author = {Narutaka Ozawa},
journal= {arXiv preprint arXiv:math/0210411},
year = {2007}
}
Comments
4 pages. Largely revised to include an account for the construction of uncountably many simple T groups