On integrability of transverse Lie–Poisson structures at nilpotent elements

Yassir Dinar

doi:10.1016/j.geomphys.2020.103690

On integrability of transverse Lie–Poisson structures at nilpotent elements

Yassir Dinar

Mathematics

Research output: Contribution to journal › Article › peer-review

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.

Original language	English (US)
Article number	103690
Journal	Journal of Geometry and Physics
Volume	155
DOIs	https://doi.org/10.1016/j.geomphys.2020.103690
State	Published - Sep 2020

Keywords

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

ASJC Scopus subject areas

Mathematical Physics
General Physics and Astronomy
Geometry and Topology

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10.1016/j.geomphys.2020.103690

Cite this

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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.",

keywords = "Argument shift method, Completely integrable system, Finite W-algebra, Nilpotent elements of semisimple type, Polynomial Poisson brackets, Slodowy slice",

author = "Yassir Dinar",

note = "Publisher Copyright: {\textcopyright} 2020 Elsevier B.V.",

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AB - 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.

KW - Argument shift method

KW - Completely integrable system

KW - Finite W-algebra

KW - Nilpotent elements of semisimple type

KW - Polynomial Poisson brackets

KW - Slodowy slice

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JO - Journal of Geometry and Physics

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ER -

On integrability of transverse Lie–Poisson structures at nilpotent elements

Abstract

Keywords

ASJC Scopus subject areas

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