Abstract

The 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.

Full Text
Published version (Free)

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call