On integrability of transverse Lie-Poisson structures at nilpotent elements

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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Cited by in corpus (1)

• Low dimensional bihamiltonian structures of topological type