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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

Let G be a Lie groupoid. Recall that the associated adiabatic groupoid G ad is the groupoid obtained by the deformation to the normal cone construction corresponding to the inclusion G (0) → G. In the present paper, we consider the crossed product G ga of the natural action of R * + on the adiabatic groupoid G ad 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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hal-03776357 , version 1 (13-09-2022)

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Paternité - Pas d'utilisation commerciale - Pas de modification

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Claire Debord, Georges Skandalis. Adiabatic groupoid, crossed product by R + ⁎ and pseudodifferential calculus. Advances in Mathematics, 2014, 257, pp.66-91. ⟨10.1016/j.aim.2014.02.012⟩. ⟨hal-03776357⟩
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