This article is cited in 11 papers

Extensions of Lie algebras and Hamiltonian systems

V. V. Trofimov


Abstract: An extension $\Omega(G)$ is constructed for a Lie algebra $G$, and an algorithm is proposed which converts functions in involution on $G^*$ into functions in involution on $\Omega(G)^*$. Operators of “rigid body” type are constructed for $\Omega(G)$ in the case of a semisimple Lie algebra $G$; complete integrability is proved for the Euler equations on $\Omega(G)^*$ with these operators.
Bibliography: 21 titles.

UDC: 513.944

MSC: Primary 58F07; Secondary 17B99

Received: 16.02.1981

 English version: Mathematics of the USSR-Izvestiya, 1984, 23:3, 561–578

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