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34 pages, Pacific journal of Mathematics, Volume 189, No. 1 (1999), 117-152

Abstract:

The authors construct an algebra of pseudo-differential operators on each groupoid in a class that generalizes differentiable groupoids in order to allow the construction of manifolds with corners. The subalgebra of regularizing operators is then identified with the smooth algebra of the groupoid, as in non-commutative geometry. The construction of the algebra utilizes the Poisson algebra of functions defined on the dual of the Lie algebroid of the groupoid.

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http://nyjm.albany.edu:8000/PacJ/1999/189-1-7.html

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