A Tannaka Theorem for Proper Lie Groupoids
Abstract
By replacing the category of smooth vector bundles over a manifold with the category of what we call smooth Euclidean fields, which is a proper enlargement of the former, and by considering smooth actions of Lie groupoids on smooth Euclidean fields, we are able to prove a Tannaka duality theorem for proper Lie groupoids. The notion of smooth Euclidean field we introduce here is the smooth, finite dimensional analogue of the usual notion of continuous Hilbert field.
 Publication:

arXiv eprints
 Pub Date:
 September 2008
 arXiv:
 arXiv:0809.4423
 Bibcode:
 2008arXiv0809.4423T
 Keywords:

 Mathematics  Representation Theory;
 Mathematics  Category Theory;
 58H05;
 18D10
 EPrint:
 47 pages