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Regular and Chaotic Dynamics, 2023, Volume 28, Issue 1, Pages 44–61
DOI: https://doi.org/10.1134/S1560354723010045
(Mi rcd1194)
 

This article is cited in 1 scientific paper (total in 1 paper)

Integrable Systems Associated to the Filtrations of Lie Algebras

Bozidar Jovanovića, Tijana Šukilovićb, Srdjan Vukmirovićb

a Mathematical Institute, Serbian Academy of Sciences and Arts, Kneza Mihaila 36, 11000 Belgrade, Serbia
b Faculty of Mathematics, University of Belgrade, Studentski trg 16, 11000 Belgrade, Serbia
Citations (1)
References:
Abstract: In 1983 Bogoyavlenski conjectured that, if the Euler equations on a Lie algebra $\mathfrak{g}_0$ are integrable, then their certain extensions to semisimple lie algebras $\mathfrak{g}$ related to the filtrations of Lie algebras $\mathfrak{g}_0\subset\mathfrak{g}_1\subset\mathfrak{g}_2\dots\subset\mathfrak{g}_{n-1}\subset \mathfrak{g}_n=\mathfrak{g}$ are integrable as well. In particular, by taking $\mathfrak{g}_0=\{0\}$ and natural filtrations of ${\mathfrak{so}}(n)$ and $\mathfrak{u}(n)$, we have Gel’fand – Cetlin integrable systems. We prove the conjecture for filtrations of compact Lie algebras $\mathfrak{g}$: 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: noncommutative integrability, invariant polynomials, Gel’fand – Cetlin systems.
Funding agency Grant number
Science Fund of the Republic of Serbia 7744592
This research is supported by Project 7744592 MEGIC, Integrability and Extremal Problems in Mechanics, Geometry and Combinatorics, of the Science Fund of Serbia.
Received: 29.09.2022
Accepted: 11.01.2023
Bibliographic databases:
Document Type: Article
Language: English
Citation: Bozidar Jovanović, Tijana Šukilović, Srdjan Vukmirović, “Integrable Systems Associated to the Filtrations of Lie Algebras”, Regul. Chaotic Dyn., 28:1 (2023), 44–61
Citation in format AMSBIB
\Bibitem{JovSukVuk23}
\by Bozidar Jovanovi\'c, Tijana {\v S}ukilovi\'c, Srdjan Vukmirovi\'c
\paper Integrable Systems Associated to the Filtrations
of Lie Algebras
\jour Regul. Chaotic Dyn.
\yr 2023
\vol 28
\issue 1
\pages 44--61
\mathnet{http://mi.mathnet.ru/rcd1194}
\crossref{https://doi.org/10.1134/S1560354723010045}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4559068}
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  • https://www.mathnet.ru/eng/rcd/v28/i1/p44
  • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Abstract page:86
    References:28
     
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