Groupoid representations and modules over the convolution algebras

Details Groupoid representations and modules over the convolution algebras Groupoid representations and modules over the convolution algebras

2008-06-11

arxiv.org/abs/0806.1832v1

Mathematics

K-Theory and Homology

Scientific paper

The classical Serre-Swan's theorem defines a bijective correspondence between vector bundles and finitely generated projective modules over the algebra of continuous functions on some compact Hausdorff topological space. We extend these results to obtain a correspondence between the category of representations of an etale Lie groupoid and the category of modules over its convolution algebra that are of finite type and of constant rank. Both of these constructions are functorially defined on the Morita bicategory of etale Lie groupoids and the given correspondence represents a natural equivalence between them.

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