Queer Poisson brackets

Beltiţă, Daniel; Goliński, Tomasz; Tumpach, Alice-Barbara

Document type :

Article dans une revue scientifique: Article original

DOI :

10.1016/j.geomphys.2018.06.013

Permalink :

http://hdl.handle.net/20.500.12210/121561

Title :

Queer Poisson brackets

Author(s) :

Beltiţă, Daniel [Auteur]
Goliński, Tomasz [Auteur]
Tumpach, Alice-Barbara [Auteur]
Institut CNRS-PAULI [ICP]
Laboratoire Paul Painlevé - UMR 8524 [LPP]

Journal title :

Journal of Geometry and Physics

Pages :

358-362

Publisher :

Elsevier

Publication date :

2018-10

ISSN :

0393-0440

HAL domain(s) :

Mathématiques [math]

English abstract : [en]

We give a method to construct Poisson brackets on Banach manifolds , for which the value of at some point may depend on higher order derivatives of the smooth functions and not only on the first-order derivatives, as it ...
Show more >We give a method to construct Poisson brackets on Banach manifolds , for which the value of at some point may depend on higher order derivatives of the smooth functions and not only on the first-order derivatives, as it is the case on all finite-dimensional manifolds. We discuss specific examples in this connection, as well as the impact on the earlier research on Poisson geometry of Banach manifolds. Those brackets are counterexamples to the claim that the Leibniz property for any Poisson bracket on a Banach manifold would imply the existence of a Poisson tensor for that bracket.Show less >

Language :

Anglais

Peer reviewed article :

Oui

Audience :

Internationale

Popular science :

Non

ANR Project :

Centre Européen pour les Mathématiques, la Physique et leurs Interactions

Collections :