Some remarks about the weak containment property for groupoids and semigroups

Claire Anantharaman-Delaroche (1)

1 MAPMO - Mathématiques - Analyse, Probabilités, Modélisation - Orléans

A locally compact groupoid is said to have the weak containment property if its full C *-algebra coincide with its reduced one. Although it is now known that this property is strictly weaker than amenability, we show that the two properties are the same under a mild exactness assumption. Then we apply our result to get informations about the corresponding weak containment property for some semigroups.

Mots clés: groupoids; semigroups; weak containment; amenability

Domaines: Algèbres d'opérateurs [math.OA]; Théorie des groupes [math.GR]

Claire Anantharaman-Delaroche. Some remarks about the weak containment property for groupoids and semigroups. 2019. ⟨hal-01298838v4⟩