On classification of discrete, scalar-valued Poisson brackets
type: Item
instance of: scholarly article
title: On classification of discrete, scalar-valued Poisson brackets
zbMATH Open document ID: 1247.53095
author: E. Parodi
published in: Journal of Geometry and Physics
publication date: 2012-08-20T00:00:00Z
full work available at URL: https://arxiv.org/abs/1109.4327
review text: This paper gives a classification of discrete and scalar-valued Poisson brackets. Let us recall that he Poisson brackets were introduced by Drubovin as a dicretization of the differential geometric Poisson brackets. In this work, the author describes a procedure to classify discrete differential-geometric Poisson brackets of any order on a target space of dimension 1. Then, using a change of coordinates, he proves that any scalar-valued Poisson bracket can be reduced to the cubic Poisson bracket of a Volterra lattice. Finally, the notion of admissible Lie-Poisson groups is introduced and a procedure to produce new classes of non degenerate vector-valued first order differential geometric Poisson brackets is described.
reviewed by: Angela Gammella-Mathieu
Mathematics Subject Classification ID: 53D17
Mathematics Subject Classification ID: 53C17
zbMATH DE Number: 6069294
zbMATH Keywords: discrete Poisson brackets
zbMATH Keywords: Volterra lattice
zbMATH Keywords: Poisson-Lie group
MaRDI profile type: Publication
OpenAlex ID: W1985586541
arXiv ID: 1109.4327
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DOI: 10.1016/J.GEOMPHYS.2012.05.004
description: scientific article; zbMATH DE number 6069294