Geodesic
Integrability of the Euler equations associated with filtrations of semisimple Lie algebras
Sbornik. Mathematics, Tome 53 (1986) no. 2, pp. 541-549

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Bogoyavlenskii proposed for symmetric operators a construction connected with filtrations of Lie algebras, for which the Euler equations have a large set of integrals. In this article integrability in the Liouville sense is proved for the Euler equations on a semisimple Lie algebra with symmetric operator constructed from a filtration of Lie algebras that is connected with a chain of involution automorphisms. Bibliography: 9 titles. 
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     author = {I. V. Mykytyuk},
     title = {Integrability of the {Euler} equations associated with filtrations of semisimple {Lie} algebras},
     journal = {Sbornik. Mathematics},
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I. V. Mykytyuk. Integrability of the Euler equations associated with filtrations of semisimple Lie algebras. Sbornik. Mathematics, Tome 53 (1986) no. 2, pp. 541-549. http://geodesic.mathdoc.fr/item/SM_1986_53_2_a14/