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Symplectic structure of orbits of a co-adjoint representation of Lie algebras of type \(E\times_{\rho}G\)

For a given finite-dimensional Lie algebra G of integrals of a Hamiltonian dynamical system the author constructs a commutative finite- dimensional algebra of rational functions on the dual space \(G^*\) allowing to pass from non-commutative integration of the system to commutative one. The cases when G is the semidirect product of an Abelian algebra E
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