On duality between étale groupoids and Hopf algebroids |
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Authors: | Janez Mr?un |
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Institution: | Department of Mathematics, University of Ljubljana, Jadranska 19, 1000 Ljubljana, Slovenia |
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Abstract: | For any étale Lie groupoid G over a smooth manifold M, the groupoid convolution algebra of smooth functions with compact support on G has a natural coalgebra structure over the commutative algebra which makes it into a Hopf algebroid. Conversely, for any Hopf algebroid A over we construct the associated spectral étale Lie groupoid over M such that is naturally isomorphic to G. Both these constructions are functorial, and is fully faithful left adjoint to . We give explicit conditions under which a Hopf algebroid is isomorphic to the Hopf algebroid of an étale Lie groupoid G. |
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Keywords: | Primary 22A22 16W30 secondary 58H05 81R60 |
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