Geodesic
Integrable Euler equations associated with filtrations of Lie algebras
Sbornik. Mathematics, Tome 49 (1984) no. 1, pp. 229-238 
O. I. Bogoyavlenskii. Integrable Euler equations associated with filtrations of Lie algebras. Sbornik. Mathematics, Tome 49 (1984) no. 1, pp. 229-238. http://geodesic.mathdoc.fr/item/SM_1984_49_1_a13/
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     title = {Integrable {Euler} equations associated with filtrations of {Lie} algebras},
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Voir la notice de l'article provenant de la source Math-Net.Ru

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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[6] by Трофимов В. В. “Uravneniya Eilera na borelevskikh podalgebrakh poluprostykh algebr Li”, Izv. AN SSSR. Seriya matem, 43 (1979), 714–732 | Zbl

[7] Pevtsova T. A., “Odin sposob postroeniya kommutativnoi algebry integralov na algebrakh Li”, VII Vsesoyuznaya konferentsiya po sovremennym problemam geometrii, Minsk, 1979, 149

[8] Zhelobenko D. P., Kompaktnye gruppy Li i ikh predstvaleniya, Nauka, M., 1970 | MR | Zbl

[9] Burbaki N., Gruppy i algebry Li /Perevod s frants. pod red. A. I. Kostrikina, Mir, M., 1972 | MR | Zbl

[10] Mescheryakov M. V., “Integrirovanie uravnenii geodezicheskikh levoinvariantnykh metrik na prostykh algebrakh Li s pomoschyu spetsialnykh funktsii”, Matem. sb., 117(159) (1982), 481–493 | Zbl