Speaker: **Alexander Kumjian** (Univ. Nevada, Reno)

Title: A Stabilization Theorem for Fell Bundles over Groupoids

Time/Date: 4:45-6:15pm, Wednesday, January 13, 2016

Room: 118 Math. Sci. Building

Abstract:
We study the ideal structure of the C^{*}-algebra associated
to an upper-semicontinuous Fell bundle over a second-countable
Hausdorff groupoid. Based on ideas going back to the Packer-Raeburn
"Stabilization Trick", we construct from each such bundle a groupoid
dynamical system whose associated Fell bundle is equivalent to the
original bundle. It follows that the full and reduced C^{*}-algebras
of any saturated upper-semicontinuous Fell bundle are stably
isomorphic to the full and reduced crossed products of an associated
dynamical system. We apply our results to describe the lattice of
ideals of the C^{*}-algebra of a continuous Fell-bundle by applying
Renault's results about the ideals of the C^{*}-algebra of groupoid
crossed product. Some applications to determining the ideal structure
of twisted k-graph algebras will also be discussed.

This is joint work with Marius Ionescu, Aidan Sims and Dana Williams.