#### Vol. 316, No. 2, 2022

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A Serre–Swan theorem for coisotropic algebras

### Marvin Dippell, Felix Menke and Stefan Waldmann

Vol. 316 (2022), No. 2, 277–306
##### Abstract

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 $M$, a submanifold $C$ and an integrable smooth distribution $D\subseteq TC$ with vector bundles over this geometric situation and show an equivalence of categories for the case of a simple distribution.

##### Keywords
coisotropic algebra, projective coisotropic module, Serre–Swan theorem, foliation, vector bundles
##### Mathematical Subject Classification
Primary: 13C10
Secondary: 14D21, 16D40, 53B05, 53C12, 53D17