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.
|Number of pages||17|
|Journal||Annals of Global Analysis and Geometry|
|State||Published - 1 Nov 2020|
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.
© 2020, Springer Nature B.V.
- Contravariant derivative
- Hamiltonian system
- Poisson algebra
- Poisson submanifold