Geodesic
Extensions of Lie algebras and Hamiltonian systems
Izvestiya. Mathematics , Tome 23 (1984) no. 3, pp. 561-578

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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. 
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     author = {V. V. Trofimov},
     title = {Extensions of {Lie} algebras and {Hamiltonian} systems},
     journal = {Izvestiya. Mathematics },
     pages = {561--578},
     publisher = {mathdoc},
     volume = {23},
     number = {3},
     year = {1984},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1984_23_3_a8/}
}
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V. V. Trofimov. Extensions of Lie algebras and Hamiltonian systems. Izvestiya. Mathematics , Tome 23 (1984) no. 3, pp. 561-578. http://geodesic.mathdoc.fr/item/IM2_1984_23_3_a8/