Non-Hausdorff groupoids, proper actions and K-theory

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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 $C*_r(G_1)$ to $C^*_r(G_2)$, and thus two Morita equivalent groupoids have Morita-equivalent $C^*$-algebras.
32 pages; short version; bibliographic references added

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Operator Algebras, K-Theory and Homology, 22A22 (Primary) 46L05, 46L80, 54D35 (Secondary)

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http://salesiana.dossiersoluciones.com/handle/123456789/70345

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0403071
 http://arxiv.org/abs/math/0403071

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arXiv