Integrable systems on semidirect product Lie groups

S, CAPRIOTTI; H. MONTANI

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL

IOP PUBLISHING LTD

Lugar: Londres; Año: 2014 vol. 47 p. 1 - 23

1751-8113

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 such 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.