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Izv. Akad. Nauk SSSR Ser. Mat., 1983, Volume 47, Issue 6, Pages 1303–1321 (Mi izv1465)  

This article is cited in 7 scientific papers (total in 7 papers)

Extensions of Lie algebras and Hamiltonian systems

V. V. Trofimov


Abstract: An extension $\Omega(G)$ is constructed for a Lie algebra $G$, and an algorithm is proposed which converts functions in involution on $G^*$ into functions in involution on $\Omega(G)^*$. Operators of “rigid body” type are constructed for $\Omega(G)$ in the case of a semisimple Lie algebra $G$; complete integrability is proved for the Euler equations on $\Omega(G)^*$ with these operators.
Bibliography: 21 titles.

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English version:
Mathematics of the USSR-Izvestiya, 1984, 23:3, 561–578

Bibliographic databases:

UDC: 513.944
MSC: Primary 58F07; Secondary 17B99
Received: 16.02.1981

Citation: V. V. Trofimov, “Extensions of Lie algebras and Hamiltonian systems”, Izv. Akad. Nauk SSSR Ser. Mat., 47:6 (1983), 1303–1321; Math. USSR-Izv., 23:3 (1984), 561–578

Citation in format AMSBIB
\Bibitem{Tro83}
\by V.~V.~Trofimov
\paper Extensions of Lie algebras and Hamiltonian systems
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1983
\vol 47
\issue 6
\pages 1303--1321
\mathnet{http://mi.mathnet.ru/izv1465}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=727757}
\zmath{https://zbmath.org/?q=an:0578.58023|0547.58024}
\transl
\jour Math. USSR-Izv.
\yr 1984
\vol 23
\issue 3
\pages 561--578
\crossref{https://doi.org/10.1070/IM1984v023n03ABEH001786}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    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. V. V. Trofimov, “Canonical coordinates on orbits of the coadjoint representation of tensorial extensions of Lie groups”, Russian Math. Surveys, 49:1 (1994), 251–253  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    3. T. L. Mordasheva, “Canonical coordinates on orbits of a co-adjoint representation of certain semidirect products of Lie groups”, Russian Math. Surveys, 50:6 (1995), 1282–1283  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    4. M. A. Ramazanov, “Canonical coordinates on the orbits of the co-adjoint representation of tensor extensions of special nilpotent Lie groups of dimension nine”, Russian Math. Surveys, 51:1 (1996), 160–161  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    5. T. L. Melekhina, “Construction of canonical coordinates on the orbits of the coadjoint representation of tensor extensions of Lie groups”, Math. Notes, 64:2 (1998), 272–275  mathnet  crossref  crossref  mathscinet  zmath  isi
    6. D. V. Georgievskii, M. V. Shamolin, “Valerii Vladimirovich Trofimov”, Journal of Mathematical Sciences, 154:4 (2008), 449–461  mathnet  crossref  mathscinet  zmath
    7. V. V. Trofimov, M. V. Shamolin, “Geometric and dynamical invariants of integrable Hamiltonian and dissipative systems”, J. Math. Sci., 180:4 (2012), 365–530  mathnet  crossref  mathscinet
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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