Dazord, Pierre; Lu, Jiang-Hua; Sondaz, Daniel; Weinstein, Alan Affinoïdes de Poisson. (Affinoid Poisson structures). (French) Zbl 0728.58013 C. R. Acad. Sci., Paris, Sér. I 312, No. 7, 523-527 (1991). 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) Cited in 2 ReviewsCited in 2 Documents MSC: 37J99 Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems 58H05 Pseudogroups and differentiable groupoids 22A22 Topological groupoids (including differentiable and Lie groupoids) Keywords:affinoid space; Lie affinoid; Poisson groupoid; pregroupoid; symplectic groupoid; hamiltonian systems; Morita equivalence Citations:Zbl 0576.57023 PDFBibTeX XMLCite \textit{P. Dazord} et al., C. R. Acad. Sci., Paris, Sér. I 312, No. 7, 523--527 (1991; Zbl 0728.58013)