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# 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)
(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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