Almost Lie structures on an anchored Banach bundle
type: Item
instance of: scholarly article
title: Almost Lie structures on an anchored Banach bundle
zbMATH Open document ID: 1262.53077
author: F. Pelletier
author: P. Cabau
published in: Journal of Geometry and Physics
publication date: 2012-09-26T00:00:00Z
full work available at URL: https://arxiv.org/abs/1111.5908
review text: Several geometric structures on anchor bundles are generalized to the setting of Banach manifolds. In order to adapt results from the finite-dimensional case to this Banach framework, additional natural assumptions are imposed. The following are results distinguished by the authors: the equivalence between almost Lie-Banach algebroid structure on a bundle and Poisson structure on the dual bundle; the construction of a unique bracket and a Banach anchored bundle associated to a given derivation, and the affine structure of the set of all almost Lie brackets on an anchored Banach bundle. As applications of these results, the classical formalism for mechanical systems is also adapted. This formalism includes Hamiltonian systems, Hamilton-Jacobi equation, Lagrangian system and Euler-Lagrange equation. Finally, an interesting example, the problem of the Hilbert snake, shows how the results on Riemannian almost Lie algebroids can be applied.
reviewed by: Eduardo Chiumiento
Mathematics Subject Classification ID: 53D17
Mathematics Subject Classification ID: 58B20
zbMATH DE Number: 6086945
zbMATH Keywords: Banach manifold
zbMATH Keywords: Banach vector bundle
zbMATH Keywords: almost Lie bracket
zbMATH Keywords: almost Banach Lie algebroid
zbMATH Keywords: Hilbert snake
MaRDI profile type: Publication
OpenAlex ID: W2091770208
arXiv ID: 1111.5908
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DOI: 10.1016/J.GEOMPHYS.2012.06.005
description: scientific article; zbMATH DE number 6086945