Jean-Louis Tu

摘要

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.