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Article Dans Une Revue Advances in Mathematics Année : 2014

Adiabatic groupoid, crossed product by $\R_+^*$ and Pseudodifferential calculus

Claire Debord
Georges Skandalis
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Résumé

We consider the crossed product $G_{ga}$ by $\R_+^*$ of the adiabatic groupoid associated with any Lie groupoid $G$. We construct an explicit Morita equivalence between the exact sequence of order $0$ pseudodifferential operators on $G$ and (a restriction of) the natural exact sequence associated with $G_{ga}$. As an important intermediate step, we express a pseudodifferential operator on $G$ as an integral associated to a smoothing operator on the adiabatic groupoid $G_{ad}$ of $G$.
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Dates et versions

hal-00847432 , version 1 (23-07-2013)
hal-00847432 , version 2 (09-10-2013)
hal-00847432 , version 3 (27-09-2022)

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Claire Debord, Georges Skandalis. Adiabatic groupoid, crossed product by $\R_+^*$ and Pseudodifferential calculus. Advances in Mathematics, 2014, ⟨10.1016/j.aim.2014.02.012⟩. ⟨hal-00847432v3⟩
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