Journal of Operator Theory
Volume 74, Issue 1, Summer 2015 pp. 213-245.
Nuclearity and exactness for groupoid crossed
products
Authors:
Scott M. LaLonde
Author institution:Department of Mathematics, The University of Texas
at Tyler, 3900 University Boulevard, Tyler, TX 75799, U.S.A.
Summary: Let $(\mathcal{A}, G, \alpha)$ be a groupoid dynamical
system. We show that if $G$ is assumed to be measurewise amenable and the
section algebra $A = \Gamma_0(G^{\scriptscriptstyle{(0)}},
\mathcal{A})$ is nuclear, then the associated groupoid crossed
product is also
nuclear. This generalizes an earlier result of Green for
crossed products by locally compact groups. We also extend a
related result of
Kirchberg to groupoids. In particular, if $A$ is
exact and $G$ is amenable, then we show that
$\mathcal{A} \rtimes G$ is exact.
DOI: http://dx.doi.org/10.7900/jot.2014jun06.2032
Keywords: groupoid crossed product, $C_0(X)$-algebra, nuclearity,
exactness, exact groupoid
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