Coactions of Hopf C*-bimodules

Abstract

Coactions of Hopf C*-bimodules simultaneously generalize coactions of Hopf C*-algebras and actions of groupoids. Following an approach of Baaj and Skandalis, we construct reduced crossed products and establish a duality for fine coactions. Examples of coactions arise from Fell bundles on groupoids and actions of a groupoid on bundles of C*-algebras. Continuous Fell bundles on an etale groupoid correspond to coactions of the reduced groupoid algebra, and actions of a groupoid on a continuous bundle of C*-algebras correspond to coactions of the function algebra.

44 pages, to appear in the Journal of Operator theory

References in corpus (2)

• The relative tensor product and a minimal fiber product in the setting of $C^{\ast }$-algebras
• C*-pseudo-multiplicative unitaries and Hopf C*-bimodules

Cited by in corpus (4)

• The relative tensor product and a minimal fiber product in the setting of $C^{\ast }$-algebras
• C*-pseudo-multiplicative unitaries and Hopf C*-bimodules
• Équivalence monoïdale de groupes quantiques et K-théorie bivariante
• Locally compact quantum groupoid