Alain Connes introduced the use of Lie groupoids in noncommutative geometry in his pioneering work on the index theory of foliations. In the present paper, we recall the basic notion involved: groupoids, their C *-algebras, their pseudodifferential calculus, etc. We review several recent and older advances on the involvement of Lie groupoids in noncommutative geometry. We then propose some open questions and possible developments of the subject.
CITATION STYLE
Debord, C., & Skandalis, G. (2020). Lie groupoids, pseudodifferential calculus, and index theory. In Advances in Noncommutative Geometry: On the Occasion of Alain Connes’ 70th Birthday (pp. 245–289). Springer International Publishing. https://doi.org/10.1007/978-3-030-29597-4_4
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