Geodesic
Non-Hausdorff groupoids, proper actions and $K$-theory
Documenta mathematica, Tome 9 (2004), pp. 565-597.

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

Summary: Let $G$ be a (not necessarily Hausdorff) locally compact groupoid. We introduce a notion of properness for $G$, which is invariant under Morita-equivalence. We show that any generalized morphism between two locally compact groupoids which satisfies some properness conditions induces a $C^*$-correspondence from $C^*_r(G_2)$ to $C^*_r(G_1)$, and thus two Morita equivalent groupoids have Morita-equivalent $C^*$-algebras.
Classification : 22A22, 46L05, 46L80, 54D35
Keywords: groupoid, $C^*$-algebra, $K$-theory 
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     author = {Tu, Jean-Louis},
     title = {Non-Hausdorff groupoids, proper actions and $K$-theory},
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     url = {http://geodesic.mathdoc.fr/item/DOCMA_2004__9__a4/}
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Tu, Jean-Louis. Non-Hausdorff groupoids, proper actions and $K$-theory. Documenta mathematica, Tome 9 (2004), pp. 565-597. http://geodesic.mathdoc.fr/item/DOCMA_2004__9__a4/