On integrability of transverse Lie–Poisson structures at nilpotent elements

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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.

Original languageEnglish
Article number103690
JournalJournal of Geometry and Physics
Volume155
DOIs
Publication statusPublished - 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
  • Physics and Astronomy(all)
  • Geometry and Topology

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