Groupoids associated to semigroup actions

Jean Renault (1) , S. Sundar (2)

1 MAPMO - Mathématiques - Analyse, Probabilités, Modélisation - Orléans
2 Chennai Mathematical Institute [Inde]

In this paper, we consider topological semigroup actions on compact topological spaces. Under mild assumptions on the semigroup and the action, we construct a semi-direct product groupoid with a Haar system. We also show that it is equivalent to a transformation groupoid. We apply this construction to the Wiener-Hopf $C^{*}$-algebras.

Mots clés: Wiener-Hopf C*-algebras

Domaines: Algèbres d'opérateurs [math.OA]

Jean Renault, S. Sundar. Groupoids associated to semigroup actions. Journal of Operator Theory, 2015, Journal of Operator Theory, 73 (2), pp.491-514. ⟨hal-00963865⟩