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Algebraic properties of compatible Poisson brackets

Algebraic properties of compatible Poisson brackets We discuss algebraic properties of a pencil generated by two compatible Poisson tensors A(x) and B(x). From the algebraic viewpoint this amounts to studying the properties of a pair of skew-symmetric bilinear forms A and B defined on a finite-dimensional vector space. We describe the Lie group G P of linear automorphisms of the pencil P = {A + λB}. In particular, we obtain an explicit formula for the dimension of G P and discuss some other algebraic properties such as solvability and Levi-Malcev decomposition. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Regular and Chaotic Dynamics Springer Journals

Algebraic properties of compatible Poisson brackets

Regular and Chaotic Dynamics , Volume 19 (3) – Jun 6, 2014

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References (42)

Publisher
Springer Journals
Copyright
Copyright © 2014 by Pleiades Publishing, Ltd.
Subject
Mathematics; Dynamical Systems and Ergodic Theory
ISSN
1560-3547
eISSN
1468-4845
DOI
10.1134/S1560354714030010
Publisher site
See Article on Publisher Site

Abstract

We discuss algebraic properties of a pencil generated by two compatible Poisson tensors A(x) and B(x). From the algebraic viewpoint this amounts to studying the properties of a pair of skew-symmetric bilinear forms A and B defined on a finite-dimensional vector space. We describe the Lie group G P of linear automorphisms of the pencil P = {A + λB}. In particular, we obtain an explicit formula for the dimension of G P and discuss some other algebraic properties such as solvability and Levi-Malcev decomposition.

Journal

Regular and Chaotic DynamicsSpringer Journals

Published: Jun 6, 2014

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