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New examples of integrable Hamiltonian systems on semidirect sums of Lie algebras
Sbornik. Mathematics, Tome 80 (1995) no. 1, pp. 247-254 Cet article a éte moissonné depuis la source Math-Net.Ru

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It is shown that the argument translation method enables the construction of completely integrable Hamiltonian systems on $\mathrm{Ad}^*$-orbits of the semidirect sums $G\underset\rho{+}V$, where $G$ is an exceptional simple Lie algebra, and $\rho\colon G\to\mathrm{GL}(V)$ an irreducible representation. 
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     title = {New examples of integrable {Hamiltonian} systems on semidirect sums of {Lie} algebras},
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B. Priwitzer. New examples of integrable Hamiltonian systems on semidirect sums of Lie algebras. Sbornik. Mathematics, Tome 80 (1995) no. 1, pp. 247-254. http://geodesic.mathdoc.fr/item/SM_1995_80_1_a12/

[1] Andreev E. M., Vinberg E. B., Elashvili A. G., “Orbity naibolshei razmernosti lineinykh grupp Li”, Funkts. analiz, 1:4 (1967), 3–7 | MR | Zbl

[2] Vinberg E. B., Onischik A. L., Seminar po gruppam Li i algebraicheskim gruppam, Moskva, 1988

[3] Manakov S. V., “Zamechanie ob integrirovanii uravnenii Eilera dinamiki $n$-mernogo tverdogo tela”, Funkts. analiz, 10:4 (1976), 93–94 | MR | Zbl

[4] Mischenko A. S., Fomenko A. T., “Uravnenie Eilera na konechnomernykh gruppakh Li”, Izv.AN SSSR, Ser. matem., 42:2 (1978), 396–415 | MR | Zbl

[5] Fomenko A. T., Simplekticheskaya geometriya. Metody i prilozheniya, MGU, M., 1988 | MR

[6] Elashvili A. G., “Kanonicheskii vid i statsionarnye podalgebry tochek obschego polozheniya dlya prostykh lineinykh grupp Li”, Funkts. analiz, 6:1 (1972), 51–62 | MR | Zbl

[7] Bolsinov A. V., “Commutative families of fuctions related to consistent Poisson brackets”, Acta Appl. Math., 24 (1991), 253–274 | DOI | MR | Zbl

[8] Knop F., Littelmann P., “Der Grad erzeugender Funktionen von Invariantenringen”, Math. Z., 196 (1987), 211–229 | DOI | MR | Zbl

[9] Raïs M., “L'indice des produits semi-directs $E\underset \rho \to +g$”, C.R. Acad. Sc. Paris, Sect. A, 287 (1979), 195–197 | MR

[10] Tits F., Tabellen zu den einfachen Liegruppen und ihren Darstellungen, Berlin, 1967