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arXiv · 1905.01829

On integrability of transverse Lie-Poisson structures at nilpotent elements

Yassir Dinar
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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.

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BibTeXRIS

Yassir Dinar. 2019-05-06. On integrability of transverse Lie-Poisson structures at nilpotent elements. https://doi.org/10.1016/j.geomphys.2020.103690

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