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Journal of Operator Theory

Volume 73, Issue 2, Spring 2015  pp. 491-514.

Groupoids associated to Ore semigroup actions

Authors:  Jean Renault (1) S. Sundar (2)
Author institution:(1) Universite d'Orleans et CNRS (UMR 7349 et FR 2964), Departement de Mathematiques, 45067, Orleans Cedex 2, France
(2) Chennai Mathematical Institute, Siruseri, Padur, 603103, Tamilnadu, India

Summary: In this paper, we consider actions of locally compact Ore semigroups 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 Morita-equivalent to a transformation groupoid. We apply this construction to the Wiener--Hopf $C^{*}$-algebras.

Keywords: Wiener-Hopf $C^*$-algebras, semigroups, groupoids

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