This article is cited in 3 scientific papers (total in 3 papers)
Integrable Euler equations associated with filtrations of Lie algebras
O. I. Bogoyavlenskii
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.
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Mathematics of the USSR-Sbornik, 1984, 49:1, 229–238
MSC: Primary 17B20, 22E46, 34C35, 58F05; Secondary 34C40, 70E20, 35Q20
O. I. Bogoyavlenskii, “Integrable Euler equations associated with filtrations of Lie algebras”, Mat. Sb. (N.S.), 121(163):2(6) (1983), 233–242; Math. USSR-Sb., 49:1 (1984), 229–238
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\paper Integrable Euler equations associated with filtrations of Lie algebras
\jour Mat. Sb. (N.S.)
\jour Math. USSR-Sb.
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V. V. Trofimov, A. T. Fomenko, “Liouville integrability of Hamiltonian systems on Lie algebras”, Russian Math. Surveys, 39:2 (1984), 1–67
I. V. Mykytyuk, “Integrability of the Euler equations associated with filtrations of semisimple Lie algebras”, Math. USSR-Sb., 53:2 (1986), 541–549
Alekseevskii D., Putko B., “On the Completeness of Left-Invariant Pseudo-Riemannian Metrics on Lie-Groups”, Lect. Notes Math., 1453 (1990), 171–185
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