Journal of Operator Theory
Volume 81, Issue 2, Spring 2019 pp. 335-369.
Some consequences of stabilization theorem for Fell bundles
over exact groupoids
Authors:
Scott M. LaLonde
Author institution:Department of Mathematics, The University of Texas at Tyler, Tyler, TX 75799, U.S.A.
Summary: We investigate some consequences of a recent stabilization result of Ionescu, Kumjian, Sims, and Williams, which says that every
Fell bundle $C^*$-algebra is Morita equivalent to a canonical groupoid crossed product. First we use the theorem to give conditions
that guarantee the $C^*$-algebras associated to a Fell bundle are either nuclear or exact. We then show that a groupoid is exact if
and only if it is ``Fell exact'' in an appropriate sense. As an application, we show that extensions of exact groupoids are exact by
adapting a recent iterated Fell bundle construction due to Buss and Meyer.
DOI: http://dx.doi.org/10.7900/jot.2018feb08.2195
Keywords: Fell bundle, exact groupoid, groupoid crossed product, nuclearity, exactness
Contents
Full-Text PDF