Abstract : 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.
https://hal.archives-ouvertes.fr/hal-00963865 Contributor : Jean RenaultConnect in order to contact the contributor Submitted on : Monday, February 29, 2016 - 8:38:44 PM Last modification on : Tuesday, October 12, 2021 - 5:20:13 PM Long-term archiving on: : Monday, May 30, 2016 - 3:09:38 PM
Jean Renault, S. Sundar. Groupoids associated to semigroup actions. Journal of Operator Theory, Theta Foundation, 2015, Journal of Operator Theory, 73 (2), pp.491-514. ⟨hal-00963865⟩