Locally compact hypergroupoids (Q1985914)

The authors study locally compact hypergroupoids. Hypergroupoids generalize both hypergroups and groupoids. The authors assume the continuity of the map \((x, y) \mapsto \operatorname{supp}(\delta_{x} \ast \delta_{y})\) and show that the adjoint property in Renault's definition of the left Haar system follows automatically. Then, they show how to get some groupoid structures from a hypergroupoid. Finally, the authors study representations of hypergroupoids and show in particular that an irreducible representation of a compact hypergroupoid is fiberwise finite dimensional, generalizing a well-known result on compact groupoids and on compact hypergroups.