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arXiv · 1307.0122

Integrable systems on semidirect product Lie groups

S. Capriotti·H. Montani
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Abstract

We study integrable systems on the semidirect product of a Lie group and its Lie algebra as the representation space of the adjoint action. Regarding the tangent bundle of a Lie group as phase space endowed with this semidirect product Lie group structure, we construct a class of symplectic submanifolds equipped with a Dirac bracket on which integrable systems (in the Adler-Kostant-Symes sense) are naturally built through collective dynamics. In doing so, we address other issues as factorization, Poisson-Lie structures and dressing actions. We show that the procedure becomes recursive for some particular Hamilton functions, giving rise to a tower of nested integrable systems.

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S. Capriotti, H. Montani. 2013-06-29. Integrable systems on semidirect product Lie groups. https://doi.org/10.1088/1751-8113/47/20/205206

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