A Tannaka Theorem for Proper Lie Groupoids

Details A Tannaka Theorem for Proper Lie Groupoids A Tannaka Theorem for Proper Lie Groupoids

2008-09-25

arxiv.org/abs/0809.4423v1

Journal of Pure and Applied Algebra 214 (6) (2010) 750-768

Mathematics

Representation Theory

47 pages

Scientific paper

10.1016/j.jpaa.2009.08.004

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.

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