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Mat. Sb. (N.S.), 1983, Volume 121(163), Number 2(6), Pages 233–242 (Mi msb2188)  

This article is cited in 3 scientific papers (total in 3 papers)

Integrable Euler equations associated with filtrations of Lie algebras

O. I. Bogoyavlenskii


Abstract: In semisimple Lie algebras a new construction is determined for symmetric operators such that the Euler equations reduce to chains of linear dynamical systems. The construction is associated with filtrations of Lie algebras and leads in a number of cases to completely integrable Euler equations. An analogous construction associated with filtrations of diffeomorphism groups is determined for Lie algebras of vector fields on manifolds. Constructions of Euler equations having sets of additional integrals in involution are found for the classical case.
Bibliography: 10 titles.

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English version:
Mathematics of the USSR-Sbornik, 1984, 49:1, 229–238

Bibliographic databases:

UDC: 519.46+517.836
MSC: Primary 17B20, 22E46, 34C35, 58F05; Secondary 34C40, 70E20, 35Q20
Received: 18.05.1982

Citation: O. I. Bogoyavlenskii, “Integrable Euler equations associated with filtrations of Lie algebras”, Mat. Sb. (N.S.), 121(163):2(6) (1983), 233–242; Math. USSR-Sb., 49:1 (1984), 229–238

Citation in format AMSBIB
\Bibitem{Bog83}
\by O.~I.~Bogoyavlenskii
\paper Integrable Euler equations associated with filtrations of Lie algebras
\jour Mat. Sb. (N.S.)
\yr 1983
\vol 121(163)
\issue 2(6)
\pages 233--242
\mathnet{http://mi.mathnet.ru/msb2188}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=703326}
\zmath{https://zbmath.org/?q=an:0554.58029|0544.34058}
\transl
\jour Math. USSR-Sb.
\yr 1984
\vol 49
\issue 1
\pages 229--238
\crossref{https://doi.org/10.1070/SM1984v049n01ABEH002706}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. V. V. Trofimov, A. T. Fomenko, “Liouville integrability of Hamiltonian systems on Lie algebras”, Russian Math. Surveys, 39:2 (1984), 1–67  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    2. I. V. Mykytyuk, “Integrability of the Euler equations associated with filtrations of semisimple Lie algebras”, Math. USSR-Sb., 53:2 (1986), 541–549  mathnet  crossref  mathscinet  zmath
    3. Alekseevskii D., Putko B., “On the Completeness of Left-Invariant Pseudo-Riemannian Metrics on Lie-Groups”, Lect. Notes Math., 1453 (1990), 171–185  crossref  mathscinet  isi
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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