Some consequences of the stabilization theorem for Fell bundles over exact groupoids

Autor:	LaLonde, Scott M.
Rok vydání:	2017
Předmět:	Mathematics - Operator Algebras 46L55 (primary) 22A22 (Secondary)
Druh dokumentu:	Working Paper
Popis:	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 the sense that any invariant ideal gives rise to a short exact sequence of reduced Fell bundle $C^*$-algebras. 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. Comment: 30 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1710.03808 Zobrazit plný text záznamu View this record from Arxiv