This article is cited in 7 papers

Integrability of the Euler equations associated with filtrations of semisimple Lie algebras

I. V. Mykytyuk


Abstract: 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.

UDC: 512.54+517.9

MSC: Primary 17B20, 34C40; Secondary 17B40, 22E46, 58F05, 70E20, 70H99

Received: 20.09.1983

 English version: Mathematics of the USSR-Sbornik, 1986, 53:2, 541–549

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