Abstract. We shall introduce the notion of the Picard group for an inclusion of $C^*$-algebras. We shall also study its basic properties and the relation between the Picard group for an inclusion of $C^*$-algebras and the ordinary Picard group. Furthermore, we shall give some examples of the Picard groups for unital inclusions of unital $C^*$-algebras.
AMS Subject Classification
inclusions of $C^*$-algebras,
the Picard group
received 22.3.2019, revised 16.4.2019, accepted 13.5.2019. (Registered under 21/2019.)