Euler equations on Borel subalgebras of semisimple Lie algebras

A method connected with the translates of the invariants and semi-invariants of $\mathrm{Ad}^*$ is given for the construction of completely integrable dynamical systems on real forms of Borel subalgebras of semisimple complex Lie algebras. A reduction of the noncommutative Liouville theorem to the commutative case is thereby obtained for the indicated class of Lie algebras.
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