Journal of Operator Theory

Volume 51, Issue 2, Spring 2004 pp. 255-279.

Crossed products of

$C^*$ -algebras by groupoids and inverse semigroups

Authors: Mahmood Khoshkam (1) and Georges Skandalis (2)
Author institution: (1) Department of Mathematics and Statistics, University of Saskatchewan, Saskatoon, Canada
(2) Universite Denis Diderot (Paris VII) - CNRS, UFR de Mathematiques - UMR 7586, Case Postale 7012, 2, Place Jussieu, 75251 Paris, Cedex 05, France

Summary: We develop a new notion of action of inverse semigroups on

$C^*$ -algebras. The full and the reduced crossed product of a

$C^*$ -algebra by an inverse semigroup are developed. This construction unifies several notions of crossed product by inverse semigroups. Moreover, the relation between the crossed product by an inverse semigroup

$S$ and by its associated groupoid is investigated.

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