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

Tristan Bice

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.

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.

Paper Structure

This paper contains 21 sections, 119 theorems, 406 equations.

Table of Contents

  1. Fell Bundles
  2. Preliminaries
  3. Semigroupoids
  4. Banach Bundles
  5. Fell Bundles
  6. Arbitrary Sections
  7. Continuous Sections
  8. Morphisms
  9. Structured C*-Algebras
  10. Preliminaries
  11. Examples
  12. Morphisms
  13. Properties
  14. Domination
  15. Interpolation
  16. ...and 6 more sections

Key Result

Proposition 1

For any $a\in S$, there is at most one $x\in S^0$ with $(a,x)\in S^2$.

Theorems & Definitions (272)

  • Remark
  • Definition 1
  • Proposition 1
  • proof
  • Proposition 2
  • proof
  • Definition 2
  • Definition 3
  • Definition 4
  • Proposition 3
  • ...and 262 more