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

Authors: KAZUNORI KODAKA

Abstract: We shall generalize the notion of the strong Morita equivalence for coactions of a finite dimensional $C^*$-Hopf algebra on a unital $C^*$-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 $C^*$-Hopf algebra on a unital $C^*$-algebra. We shall investigate basic properties of the generalized Picard groups and clarify the relation between the generalized Picard groups and the Picard groups for unital inclusions of unital $C^*$-algebras.

Keywords: $C^*$-algebra, $C^*$-Hopf algebra, inclusion, Picard group, strong Morita equivalence

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