Geodesic
On a Construction Due to Khoshkam and Skandalis
Documenta mathematica, Tome 23 (2018), pp. 1995-2025.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

In this paper, we consider the Wiener-Hopf algebra, denoted $\mathcal{W}(A,P,G,\alpha)$, associated to an action of a discrete subsemigroup $P$ of a group $G$ on a $C^\ast$-algebra $A$. We show that $\mathcal{W}(A,P,G,\alpha)$ can be represented as a groupoid crossed product. As an application, we show that when $P=\mathbb{F}_{n}^{+}$, the free semigroup on $n$ generators, the $K$-theory of $\mathcal{W}(A,P,G,\alpha)$ and the $K$-theory of $A$ coincides.
Classification : 22A22, 54H20, 43A65, 46L55
Keywords: Wiener-Hopf $C^\ast$-algebras, semigroups, groupoid dynamical systems 
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     author = {Sundar, S.},
     title = {On a {Construction} {Due} to {Khoshkam} and {Skandalis}},
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Sundar, S. On a Construction Due to Khoshkam and Skandalis. Documenta mathematica, Tome 23 (2018), pp. 1995-2025. http://geodesic.mathdoc.fr/item/DOCMA_2018__23__a6/