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.