Dauns-Hofmann-Kumjian-Renault Duality for Fell Bundles and Structured C*-Algebras

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.

arXiv commentThis 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 Part I is now superseded by arXiv:2312.01161 "Sections of Fell Bundles over Étale Groupoids"

References in corpus (7)

• The Cuntz Semigroup and Comparison of Open Projections
• Reconstruction of groupoids and C*-rigidity of dynamical systems
• Étale groupoids and their $C^{\ast }$-algebras
• General Non-Commutative Locally Compact Locally Hausdorff Stone Duality
• An Algebraic Approach to the Weyl Groupoid
• Reconstruction of twisted Steinberg algebras
• Groupoid Models of $C^{\ast }$-algebras and Gelfand Duality