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Representations of étale Lie groupoids and modules over Hopf algebroids

Jure Kališnik (2011)

Czechoslovak Mathematical Journal

The classical Serre-Swan's theorem defines an equivalence between the category of vector bundles and the category of 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 étale Lie groupoid and the category of modules over its Hopf algebroid that are of finite type and of constant rank. Both of these constructions are functorially...

Representations of Polish groups and continuity

M. Cianfarani, J.-M. Paoli, P. Simonnet, J.-C. Tomasi (2014)

Studia Mathematica

In the first part of the paper, some criteria of continuity of representations of a Polish group in a Banach algebra are given. The second part uses the result of the first part to deduce automatic continuity results of Baire morphisms from Polish groups to locally compact groups or unitary groups. In the final part, the spectrum of an element in the range of a strongly but not norm continuous representation is described.

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