Sergio Albeverio and Shao-Ming Fei 1998 J. Phys. A: Math. Gen. 31 1211 doi:10.1088/0305-4470/31/4/010
Integrable Poisson algebras and two-dimensional manifolds
Sergio Albeverio and Shao-Ming Fei
Show affiliationsThe relations between integrable Poisson algebras with three generators and two-dimensional symplectic manifolds are investigated. It is shown that for a given integrable Poisson algebra 
there exists a two-dimensional symplectic manifold 
such that the Poisson algebra generated by the coordinates of M coincides with the algebra . Vice versa the coordinates of a given smooth two-dimensional symplectic manifold M embedded in 
generate an integrable Poisson algebra. Moreover, smooth Poisson algebraic maps between two integrable Poisson algebras are governed by equations involving the symplectic manifolds corresponding to these algebras.
- PACS
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03.65.Vf Phases: geometric; dynamic or topological
- MSC
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81S10 Geometry and quantization, symplectic methods (See also 53D50)
- Subjects
- Dates
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Issue 4 (30 January 1998)
Received 1 April 1997
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Integrable Poisson algebras and two-dimensional manifolds
Sergio Albeverio and Shao-Ming Fei 1998 J. Phys. A: Math. Gen. 31 1211
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