Abstract
We prove the noncommutative integrability of the magnetic geodesic flow defined by the Kirillov form on a coadjoint orbit of a compact semisimple Lie group. This implies that on a simply-connected homogeneous symplectic manifold the magnetic geodesic flow, defined by the homogeneous symplectic form and some metric, is integrable in the noncommutative sense.
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Original Russian Text Copyright © 2005 Efimov D. I.
The author was supported by the Russian Foundation for Basic Research (Grant 03-01-00403).
Translated from Sibirski \( \overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{\imath} \) Matematicheski \( \overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{\imath} \) Zhurnal, Vol. 46, No. 1, pp. 106–118, January–February, 2005.
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Efimov, D.I. The magnetic geodesic flow on a homogeneous symplectic manifold. Sib Math J 46, 83–93 (2005). https://doi.org/10.1007/s11202-005-0009-y
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DOI: https://doi.org/10.1007/s11202-005-0009-y