On integrability of transverse Lie-Poisson structures at nilpotent elements

JOURNAL OF GEOMETRY AND PHYSICS

卷:155

Article

Dinar, Yassir¹ 

[1] Sultan Qaboos Univ, Muscat, Oman

关键词: Completely integrable system;    Argument shift method;    Slodowy slice;    Polynomial Poisson brackets;    Nilpotent elements of semisimple type;    Finite W-algebra;   

DOI  :  10.1016/j.geomphys.2020.103690

来源: Elsevier

【 摘 要 】

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. (C) 2020 Elsevier B.V. All rights reserved.

【 授权许可】

Free