Hypergroup structures arising from certain dual objects of a hypergroup

Abstract

In the present paper hypergroup structures are investigated on distinguished dual objects related to a given hypergroup K, especially to a semi-direct product hypergroup K = H ⋊_α G defined by an action α of a locally compact group G on a commutative hypergroup H. Typical dual objects are the sets of equivalence classes of irreducible representations of K, of infinite-dimensional irreducible representations of type I hypergroups K, and of quasi-equivalence classes of type II₁ factor representations of non-type I hypergroups K. The method of proof relies on the notion of a character of a representation of K = H ⋊_α G.