symplectic groupoids
Symplectic groupoids are mathematical structures that generalize symplectic manifolds and symplectic vector spaces. They consist of a set of points equipped with a compatible symplectic form, along with a groupoid structure that encodes the symplectic geometry in a way that allows for composition of symplectic transformations. Groupoids are a generalization of groups, allowing for partial transformations and inverses. Symplectic groupoids provide a powerful framework for studying symplectic geometry and have applications in areas such as classical mechanics and geometric quantization.
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