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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