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Affinoïdes de Poisson. (Affinoid Poisson structures). (French) Zbl 0728.58013

The authors study of affinoid spaces X (pregroupoids in the sense of A. Kock, cf. also J. Pradines, Cah. Topologie Géom. Différ. Catégoriques 26, 339-380 (1985; Zbl 0576.57023)) where the graph \({\mathcal P}\) is a coisotropic (Lagrangian) submanifold. Then the quotients \(X\times_ bX/{\mathcal P}\), \(X\times_ aX/{\mathcal P}\) are Poisson (respectively symplectic) groupoids with Poisson actions on X. Relations to hamiltonian systems with symmetries and Morita equivalence of Poisson manifolds are mentioned.
Reviewer: J.Chrastina (Brno)

MSC:

37J99 Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems
58H05 Pseudogroups and differentiable groupoids
22A22 Topological groupoids (including differentiable and Lie groupoids)

Citations:

Zbl 0576.57023
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