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The generalized Picard groups for finite dimensional $C^*$-Hopf algebra coactions on unital $C^*$-algebras (1805.08358v1)
Published 22 May 2018 in math.OA
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 $C*$-algeba. 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.