## Symplectic structure of orbits of a co-adjoint representation of Lie algebras of type $$E\times_{\rho}G$$.(Russian)Zbl 0538.58013

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 and a simple algebra of types sl(2n), gl(2n) or sp(2n) irreducible actions on E are considered.
Reviewer: Yu.N.Mukhin

### MSC:

 37J99 Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems 17B10 Representations of Lie algebras and Lie superalgebras, algebraic theory (weights)
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