A Schwartz type algebra for the Tangent Groupoid
Abstract
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.
Cite
@article{arxiv.0802.3596,
title = {A Schwartz type algebra for the Tangent Groupoid},
author = {Paulo Carrillo Rouse},
journal= {arXiv preprint arXiv:0802.3596},
year = {2008}
}
Comments
To appear on the "Proceedings of the International Conference on K-theory and Non commutative geometry", VASBI, held at Valladolid Spain, September 2006"