  We construct an algebra of smooth functions over the tangent groupoid
associated to any Lie groupoid. This algebra is a field of algebras over the
closed interval [0, 1] which fiber at zero is the algebra of Schwartz functions
over the Lie algebroid, whereas any fiber out of zero is the convolution
algebra of the initial groupoid. Our motivation comes from index theory for Lie
groupoids. In fact, our construction gives an intermediate algebra between the
enveloping C-algebra and the convolution algebra of compactly supported
functions of the tangent groupoid; and it will allows us, in a further work, to
define other analytic index morphisms as a sort of deformations.
