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

2018/05/22 by Kodaka, Kazunori
#46L05 #FOS: Mathematics #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.1805.08358

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.

Related

• The Picard groups for unital inclusions of unital C^*-algebras
• Free coactions of a finite dimensional C^*-Hopf algebra and strong Morita equivalence
• The Picard groups of unital inclusions of unital C^*-algebras induced by involutive equivalence bimodules
• The strong Morita equivalence for coactions of a finite dimensional C^*-Hopf algebra on unital C^*-algebras
• Equivariant Picard groups of C^*-algebras with finite dimensional C^*-Hopf algebra coactions