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A Serre–Swan theorem
for coisotropic algebras
Marvin Dippell, Felix Menke and Stefan Waldmann |
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Vol. 316 (2022), No. 2, 277–306
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Abstract |
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Coisotropic algebras are used to formalize coisotropic reduction in Poisson geometry and in deformation quantization; they find applications in other fields as well. Here we prove a Serre–Swan theorem relating the regular projective modules over the coisotropic algebra built out of a manifold , a submanifold and an integrable smooth distribution with vector bundles over this geometric situation and show an equivalence of categories for the case of a simple distribution. |
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Keywords
coisotropic algebra, projective coisotropic module,
Serre–Swan theorem, foliation, vector bundles
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Mathematical Subject Classification
Primary: 13C10
Secondary: 14D21, 16D40, 53B05, 53C12, 53D17
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Milestones
Received: 20 January 2021
Revised: 23 March 2021
Accepted: 25 December 2021
Published: 6 April 2022
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Authors |
| Marvin Dippell | |
| Department of Mathematics Julius Maximilian University of Würzburg Würzburg Germany |
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| Felix Menke | |
| Department of Mathematics Julius Maximilian University of Würzburg Würzburg Germany |
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| Stefan Waldmann | |
| Department of Mathematics Julius Maximilian University of Würzburg Würzburg Germany |
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