The Kahler manifolds homogeneous under the action of compact Lie groups are constructed and employed as phase spaces of dynamical systems. The corresponding Lie algebra is realized in terms of the Poisson brackets and first-order differential operators, respectively, for classical and quantal dynamics.
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Bauman Moscow State Technical University, ul. Vtoraya Baumanskaya 5, MoscowBauman Moscow State Technical University, ul. Vtoraya Baumanskaya 5, Moscow