The relative tensor product and a minimal fiber product in the setting of $C^{\ast }$-algebras

Abstract

We introduce a relative tensor product of $C^{\ast }$-modules and a spatial fiber product of $C^{\ast }$-algebras that are analogues of Connes' fusion of correspondences and the fiber product of von Neumann algebras introduced by Sauvageot, respectively, and study their categorical properties. These constructions form the basis for our approach to quantum groupoids in the setting of $C^{\ast }$-algebras that is published separately.

36 pages; completely rewritten for publication and to be more easily accessible; the main constructions and results remain unaltered; the numbering has changed; beware that existing references in other articles may refer to the (numbering of the) first version

References in corpus (5)

• Von Neumann Modules, Intertwiners and Self-Duality
• C*-pseudo-multiplicative unitaries
• Coactions of Hopf C*-bimodules
• $C^{\ast }$-pseudo-Kac systems and duality for coactions of concrete Hopf $C^{\ast }$-bimodules
• From Hopf C*-families to concrete Hopf C*-bimodules

Cited by in corpus (6)

• Coactions of Hopf C*-bimodules
• C*-pseudo-multiplicative unitaries and Hopf C*-bimodules
• Measured quantum groupoids associated to proper dynamical quantum groups
• Multiplicative partial isometries, manageability, and C*-algebraic quantum groupoids
• Locally compact quantum groupoid
• Multiplier Hopf algebroids. Basic theory and examples