Extensions of Lie algebras and Hamiltonian systems

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.