On integrability of transverse Lie-Poisson structures at nilpotent elements
Mathematical Physics
2020-06-24 v4 Differential Geometry
Dynamical Systems
math.MP
Representation Theory
Abstract
We construct families of functions in involution for transverse Poisson structures at nilpotent elements of Lie-Poisson structures on simple Lie algebras by using the argument shift method. Examples show that these families contain completely integrable systems that consist of polynomial functions. We provide a uniform construction of these integrable systems for an infinite family of distinguished nilpotent elements of semisimple type.
Cite
@article{arxiv.1905.01829,
title = {On integrability of transverse Lie-Poisson structures at nilpotent elements},
author = {Yassir Dinar},
journal= {arXiv preprint arXiv:1905.01829},
year = {2020}
}