The generalized Picard groups for finite dimensional $C^ast$ -Hopf algebra coactions on unital $C^ast$ -algebras

Abstract

We shall generalize the notion of the strong Morita equivalence for coactions of a finite dimensional $C^ast$ -Hopfalgebra on a unital $C^ast$ -algebra and define the Picard groups with respect to the generalized strong Morita equivalence.We call them the generalized Picard groups for coactions of a finite dimensional $C^ast$ -Hopf algebra on a unital $C^ast$ -algebra.We shall investigate basic properties of the generalized Picard groups and clarify the relation between the generalizedPicard groups and the Picard groups for unital inclusions of unital$C^ast$ -algebras.