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.

中文翻译：

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幂零元横向李泊松结构的可积性

摘要 我们在简单李代数上的李泊松结构的幂零元处使用参数移位方法构造横向泊松结构的对合函数族。示例表明，这些族包含由多项式函数组成的完全可积系统。我们提供了这些可积系统的统一构造，用于半简单类型的显着幂零元的无限族。