Abstract
An action of a group G on a set S is a (surjective) composition law ƒ: G × S → S, associative with respect to the group multiplication m: G × G → G. We show that an action of a Lie group G on a symplectic manifold P together with an equivariant momentum mapping can be characterized as a symplectic reduction ϱ: T* G × P → P, associative with respect to Pm, where P is the phase functor [1]. Applications to a study of symplectic analogues of pseudogroups [4] (called also quantum groups [5]) and their representations will be presented in subsequent publications.
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