Geodesic
Finite-dimensional representations of Lie algebras and completely integrable systems
Sbornik. Mathematics, Tome 39 (1981) no. 4, pp. 547-558 Cet article a éte moissonné depuis la source Math-Net.Ru

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A method is presented for constructing completely integrable dynamical systems. It employs the translates of functions on a finite-dimensional, $\operatorname{Ad}^*$-invariant subspace of the space of analytic functions on the dual space of the Lie algebra. The method is applied to the construction of completely integrable systems on real forms of Borel subalgebras of the exceptional Lie algebras. An algorithm is proposed for the calculation of the semi-invariants of the representation $\operatorname{Ad}^*$ of Borel subalgebras of the exceptional Lie algebras. Bibliography: 12 titles. 
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     author = {V. V. Trofimov},
     title = {Finite-dimensional representations of {Lie} algebras and completely integrable systems},
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V. V. Trofimov. Finite-dimensional representations of Lie algebras and completely integrable systems. Sbornik. Mathematics, Tome 39 (1981) no. 4, pp. 547-558. http://geodesic.mathdoc.fr/item/SM_1981_39_4_a6/

[1] V. I. Arnold, Matematicheskie metody klassicheskoi mekhaniki, izd-vo “Nauka”, Moskva, 1974 | MR

[2] Zh. Diksme, Universalnye obertyvayuschie algebry, izd-vo “Mir”, Moskva, 1978 | MR

[3] N. Burbaki, Gruppy i algebry Li, izd-vo “Mir”, Moskva, 1972 | MR

[4] A. S. Mischenko, A. T. Fomenko, “Obobschennyi metod Liuvillya integrirovaniya gamiltonovykh sistem”, Funk. analiz, 12:2 (1978), 46–56 | MR | Zbl

[5] A. S. Mischenko, A. T. Fomenko, “Uravneniya Eilera na konechnomernykh gruppakh Li”, Izv. AN SSSR, seriya matem., 42 (1978), 396–415 | MR | Zbl

[6] A. S. Mischenko, A. T. Fomenko, “Integriruemost uravnenii Eilera na poluprostykh algebrakh Li”, Trudy seminara po vektornomu i tenzornomu analizu, vyp. XIX, izd-vo MGU, Moskva, 1979

[7] A. A. Arkhangelskii, “Vpolne integriruemye gamiltonovy sistemy na gruppe treugolnykh matrits”, Matem. sb., 108(150) (1979), 134–142 | MR

[8] V. V. Trofimov, “Uravneniya Eilera na borelevskikh podalgebrakh poluprostykh algebr Li”, Izv. AN SSSR, seriya matem., 43 (1979), 714–732 | MR | Zbl

[9] T. A. Springer, “Some arithmetical results on semi-simple Lie algebras”, Publ. Math. Paris, 30 (1966), 115–141 | MR

[10] P. Steinberg, Lektsii o gruppakh Shevalle, izd-vo “Mir”, Moskva, 1975 | MR

[11] M. Vergene, “La structure de Poisson sur l'algèbre sumétrique d'une algèbre de Lie nilpotente”, Bull. Soc. Math. France, 100 (1972), 301–335 | MR