Using the notion of a contravariant derivative, we give some algebraic and geometric characterizations of Poisson algebras associated to the infinitesimal data of Poisson submanifolds. We show that such a class of Poisson algebras provides a suitable framework for the study of the Hamiltonization problem for the linearized dynamics along Poisson submanifolds.
Bibliographical noteFunding Information:
This work was partially supported by the Mexican National Council of Science and Technology (CONACyT) under research project CB-258302. J. C. R.-P wishes also to thank CONACyT for the postdoctoral fellowship. The authors are very grateful to an anonymous Referee for critical comments and useful observations.
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- Contravariant derivative
- Hamiltonian system
- Poisson algebra
- Poisson submanifold