Dauns-Hofmann-Kumjian-Renault Duality for Fell Bundles and Structured C*-Algebras
arXiv:2104.12415
Abstract
We unify the classic Dauns-Hofmann representation with Kumjian and Renault's Weyl groupoid representation. More precisely, we use ultrafilters to represent C*-algebras with some additional structure on Fell bundles over locally compact étale groupoids. Our construction is even functorial and thus a fully-fledged non-commutative extension of the classic Gelfand duality.
This paper will not be updated in its present form - the material will instead be revised and expanded in separate papers. Part I is now superseded by arXiv:2312.01161 "Sections of Fell Bundles over Étale Groupoids"