Exactness from Proper Actions

Details Exactness from Proper Actions Exactness from Proper Actions

2005-07-07

arxiv.org/abs/math/0507146v1

Mathematics

Operator Algebras

5 pages

Scientific paper

In this paper we show that if a discrete group $G$ acts properly
isometrically on a discrete space $X$ for which the uniform Roe algebra
$C_u^*(X)$ is exact then $G$ is an exact group. As a corollary, we note that if
the action is cocompact then the following are equivalent: The space $X$ has
Yu's property A; $C^*_u(X)$ is exact; $C_u^*(X)$ is nuclear.

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