Abstract
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.
| Original language | English |
|---|---|
| Pages (from-to) | 415-431 |
| Number of pages | 17 |
| Journal | Annals of Global Analysis and Geometry |
| Volume | 58 |
| Issue number | 4 |
| DOIs | |
| State | Published - 1 Nov 2020 |
Bibliographical note
Funding 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.
Publisher Copyright:
© 2020, Springer Nature B.V.
Keywords
- Contravariant derivative
- Hamiltonian system
- Linearization
- Poisson algebra
- Poisson submanifold