Authors: Jovanović, Božidar 
Šukilović, Tijana
Vukmirović, Srđan
Affiliations: Mechanics 
Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: Integrable Systems Associated to the Filtrations of Lie Algebras
Journal: Regular and Chaotic Dynamics
Volume: 28
Issue: 1
First page: 44
Last page: 61
Issue Date: 1-Jan-2023
Rank: M22
ISSN: 1560-3547
DOI: 10.1134/S1560354723010045
Abstract: 
In 1983 Bogoyavlenski conjectured that, if the Euler equations on a Lie algebra g are integrable, then their certain extensions to semisimple lie algebras g related to the filtrations of Lie algebras (Formula presented.)are integrable as well.In particular, by taking g0={0} and natural filtrations of so(n) and u(n), we haveGel’fand – Cetlin integrable systems. We prove the conjecturefor filtrations of compact Lie algebras g: the system is integrable in a noncommutative sense by means of polynomial integrals. Various constructions of complete commutative polynomial integrals for the system are also given.
Keywords: Gel’fand – Cetlin systems | invariant polynomials | noncommutative integrability; Nonlinear Sciences - Exactly Solvable and Integrable Systems; Nonlinear Sciences - Exactly Solvable and Integrable Systems; Mathematics - Group Theory; Mathematics - Symplectic Geometry; 37J35, 17B63, 17B80, 53D20
Publisher: Springer Link
Project: Project 7744592 MEGIC, Integrability and Extremal Problems in Mechanics, Geometry and Combinatorics, of the Science Fund of Serbia

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